Journal of Indian Acad. Math.  
Vol. 47, No. 1 (2025) pp. 41-63  
ISSN: 0970-5120  
V. Jeyanthi1  
A COMPARATIVE ANALYSIS OF SELJE  
TOPOLOGICAL SPACE WITH OTHER  
TOPOLOGICAL SPACES  
and  
N. Selva Nandhini2  
Abstract: In recent years, numerous topologies have emerged, including the  
newly discovered Selje topology, which builds on micro and nano  
topologies. This paper offers a comparative analysis of Selje topology,  
emphasizing its real-world applications, particularly in analyzing dynamic  
systems such as climate change. The fundamental principles that link Selje,  
Micro and Nano topologies are discussed. The analysis demonstrates that  
Selje topology provides a more refined and flexible framework, allowing for  
greater precision in understanding complex, multifactorial systems. Key  
findings highlight Selje’s ability to handle intricate interdependencies and  
scalability challenges more effectively than nano and micro topologies,  
making it especially valuable for studying large datasets and highly  
interconnected systems.  
Keywords: Selje Topological Space, Micro Topology, Nano Topology,  
Scalability, Precision, Inclusion.  
Mathematics Subject Classification: 54A05, 54B05.  
1. Introduction  
Topology, a branch of mathematics focused on studying properties of space that  
remain invariant under continuous deformations, has evolved significantly with the  
development of specialized topological structures. These structures have become  
essential in analyzing complex, multifactorial systems across diverse fields, such as  
engineering, medical sciences and, more recently, climate change analysis. Among  
42  
V. JEYANTHI, AND N. SELVA NANDHINI  
the notable advancements in topological spaces are nano topology, micro topology  
and the newly introduced Selje topology. Each of these topologies offers unique  
frameworks for examining spatial relationships, continuity and the interaction of  
critical variables within complex systems.  
Nano topology [12] introduced by Lellis Thivagar in 2013, relies on lower  
and upper approximations, providing a binary classification system that identifies  
whether elements belong to a critical or non-critical set. This straightforward  
structure excels in isolating key spatial elements in relatively simple systems.  
However, nano topology struggles with more complex and interdependent systems,  
as it cannot fully capture the wide range of possible relationships between elements.  
This limitation becomes especially pronounced in systems where variables interact  
dynamically and change over time.  
To overcome these limitations, micro topology [10] was developed by  
Sakkraiveeranan in 2019. Micro topology builds on the framework of nano topology  
by incorporating Levine’s generalized closed sets, which allow for more flexible and  
detailed approximations. This extension provides a deeper exploration of open and  
closed sets, making micro topology better suited for dynamic systems with greater  
complexity. While this approach offers a more refined understanding of spatial  
relationships, it still encounters difficulties when handling highly multifactorial  
systems with overlapping interdependent variables.  
In 2023, Selje topology [5] introduced by Jeyanthi and Selva Nandhini,  
emerged as a further refinement of nano and micro topologies. It was developed to  
address the challenges posed by complex systems where multiple variables interact in  
intricate ways. Selje topology builds on the strengths of its predecessors,  
incorporating Selje-open and Selje-closed sets that provide even finer approximations  
of spatial elements. This enhanced framework allows for better handling of set  
intersections and scalability, making it particularly effective in studying systems that  
involve intricate dependencies and relationships among multiple variables.  
While climate change analysis represents a key application of Selje topology,  
its usefulness extends beyond this field. The topology’s ability to manage  
multifactorial systems makes it suitable for other domains as well, including  
biological systems where gene interactions and cellular processes are interdependent.  
Similarly, in network analysis, Selje topology can provide insights into the intricate  
relationships within social or communication networks, where multiple layers of  
connection and influence must be considered. By offering a more refined and  
adaptable approach to spatial relationships, Selje topology demonstrates significant  
potential for analyzing dynamic, interconnected systems across various disciplines.  
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
43  
This paper presents a comparative analysis of nano, micro and Selje  
topologies, focusing on their respective strengths and limitations in addressing the  
complexities of climate change. By examining the foundational theorems of each  
topology and applying them to climate change impact analysis, this study aims to  
show how Selje topology offers a deeper, more flexible understanding of  
multifactorial processes. The analysis highlights the critical role of topological  
methods in detecting and analyzing the intricate patterns and relationships that define  
dynamic systems, emphasizing the practical utility of these frameworks in  
contemporary scientific research.  
Preliminaries  
Definition 2.1: Let  
V
denote a non-empty finite set of objects referred  
represent an equivalence relation on known as  
to as the universe and let  
V
the indiscernibility relation. Elements within the same equivalence class are  
considered indiscernible from each other. This pair, denoted as (V, )  
,
constitutes the approximation space.  
Let  
E
be a subset of  
V
.
1. The lower approximation of  
E
with respect to  
, denoted as (E)  
,
consists of all objects that can definitively be classified as belonging  
to  
(E) {() : () E} where  
determined by  
E
under the influence of  
. In mathematical terms,  
signifies the equivalence class  
E
.
2. The upper approximation of  
comprises all objects that could potentially be classified as  
influence of . Mathematically, (E) {() : () E  }  
E
with respect to  
, denoted as (E)  
,
E
under the  
3. The boundary region of  
includes all objects that cannot be definitively classified as either  
belonging to or not belonging to under the influence of . In  
mathematical terms, (E) (E) (E)  
E
with respect to  
, denoted as (E)  
,
E
E
44  
V. JEYANTHI, AND N. SELVA NANDHINI  
Definition 2.2: Let  
V
represent the universe,an equivalence relation  
on  
V
denote  
and T(E) {E, , (E), (E), (E)}, where E V  
.
Under these conditions, () Proceeding with the given postulates:  
1.  
and  
V
belong to (E).  
2. Any subset of the union of elements (E) remains within (E)  
.
3. Any finite subset of the intersection of elements (E) is contained  
in (E). In other words, (E) forms a topology on known as the nano  
topology on concerning (V, (E)) constitutes the nano topological  
V
V
E
.
space. The sets within (E) are denoted as nano open sets and the dual  
c
nano topology of [(E)] is represented by [(E)]  
.
In this context, T(E) is termed the Nano Topology [5] of the universal  
with respect to the subset . The pair (V, T(E)) constitutes a nano  
set  
V
E
topological space and its constituent elements are referred to as nano-open  
sets.  
Definition 2.3: (V, T(E)) creates a nanotopological space. In this  
case,  
the  
set  
Y(E)  
consists  
of  
two  
groups,  
namely  
{N (N' Y) : N, N' T(E)} . The combination T(E) is expressed as the  
microtopology  
Y
; where  
Y
is not nanotopology elements of T(E).  
Definition 2.4:  
postulates:  
Micro Topology Y(E)adheres to the following  
1. Both the universal set (E) and the empty set  
are elements of  
µ(E).  
2. Any subset of the union of elements of µ(E) remains within µ(E)  
.
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
45  
3. Any finite subset of the intersection of elements of µ(E)is contained  
within µ(E). Thus, the Micro topology µ(E) is defined as  
µ(E) {N (N' µ)} for  
N
and N' µ(E) , where µ T(E)  
.
This constitutes the Micro topology on the set  
V
concerning  
E
.
The trio (V, T(E), µ(E)) is denoted as the Micro topological space  
and the elements of µ(E)are known as Mic-open sets. Moreover, the  
complement of a Mic-open set is defined as a Mic-closed set.  
Next, Y(E)is called the microtopology of  
E
and  
V
. Triple  
(E, T(E), Y(E))called micro-topological space. Elements in Y(E) are  
slightly open and their complements are slightly off.  
Definition 2.5: Consider the microtopological space (V, Y(E)) and  
Selje topology be defined as SJ(E) {(S J) (S J') :S Y(E) and for  
fixed J,J' Y(E), J J' V}  
Definition 2.6: The Selje topology SJ(E) satisfies the following axioms  
1. Both the universal set  
V
and the empty set  
are elements of T(E).  
2. Any subset of the union of elements from SJ(E) remains within  
SJ(E)  
.
3. Any finite subset of the intersection of elements within SJ(E) is  
contained within SJ(E)  
.
The triplet (E, Y(E),SJ(E)) is labeled as Selje topological space.  
Then, the components of Selje topology are Selje-Open (SJ -Open) sets and  
46  
V. JEYANTHI, AND N. SELVA NANDHINI  
their complements are Selje-closed (SJ -closed) sets. The collection of Selje  
closed sets of Selje topology is denoted as SJCL(E)  
.
3. Theoretical Foundations and Comparative Analysis of Nano, Micro and Selje  
Topologies  
The theorems compare nano, micro and Selje Topological Spaces, showing  
that Selje Topology offers finer approximations, better scalability for complex  
systems and generalizes the other two. They demonstrate why Selje Topological  
Space is superior for handling complex, multifactorial applications with improved  
precision and flexibility.  
Theorem 3.1 establishes a hierarchical relationship between nano, micro and  
Selje Topological Spaces, showing that Selje topological space provides the most  
refined approximations, followed by micro and nano topologies. The inclusions  
between closures and interiors reflect the increasing precision of each space.  
Theorem 3.1: Inclusion in Nano, Micro and Selje Topologies: Let X U  
be a subset in the universe U. The relationships between the approximations in  
nano, micro and Selje topologies are given by:  
LR(X) Miccl(X) SJR cl(X)  
and  
SJR int(X) Micint(X) UR(X)  
where LR(X) and UR(X) are the lower and upper approximations in nano  
topology, Miccl(X) and Micint(X) are the micro closure and interior in  
micro topology and SJcl(X)and SJint(X) are the Selje closure and  
interior, respectively.  
Proof: In nano topology, L(X) X U(X)  
.
In micro topology, L(X) Miccl(X) and Micint(X) UR(X)  
.
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
47  
In Selje topology,  
Mic cl(X) SJcl(X)  
and  
SJint(X) Micint(X)  
.
Thus, the theorem follows.  
Lemma 3.2 states that if a function is continuous in nano topology, it will  
also be continuous in both micro and Selje topologies. This is because micro and  
Selje topologies generalize the structures of nano topology, preserving the continuity  
of functions across these spaces.  
Lemma 3.2 Preservation of Continuity in Micro and Selje Topologies: If  
f :U V is continuous in nano topology, then f is continuous in both micro  
and Selje topological spaces.  
Proof: In nano topology, f 1(V') R(U) for any nano-open set V' V . In  
micro topology, since micro-open sets are unions or intersections of nano-open sets,  
f 1(W') µR(U). Similarly, in Selje topology, f 1(S') SJR(U). Hence, f is  
continuous in both micro and Selje topologies.  
Theorem 3.3 demonstrates that Selje Topological Space scales better than  
nano and micro topologies. As system complexity increases, Selje retains higher  
precision in approximating sets, making it ideal for complex systems.  
Scalability here refers to how well the different topologies handle an increase  
in system complexity. As the complexity of the dataset (e.g., the number of variables,  
the amount of data) increases, the precision of approximations made by each  
topology changes.  
Theorem 3.3 Scalability of Approximations: For any subset A U , we  
have:  
lim  
precision(SJR cl(A)) precision(Miccl(A)) precision(LR(A))  
complexity(A)  
| LR(A) |  
Proof: 1. In nano topology, precision(LR(A))  
| A| .  
tends to 0 as  
| A|  
48  
V. JEYANTHI, AND N. SELVA NANDHINI  
| Miccl(A) |  
2. In micro topology, precision(Miccl(A))   
, which is more precise  
| A|  
than in nano topology.  
| SJR cl(A) |  
3. In Selje topology, precision (SJcl(A))   
, which remains precise  
| A|  
even as complexity increases.  
Theorem 3.4 shows that the intersection of Selje-open sets provides a finer  
approximation than nano-open or micro-open sets. Selje Topology captures more  
intricate relationships, making it more powerful for handling complex data.  
Theorem 3.4 Finer Set Operations in Selje Topology: For any subsets  
A, B U , the intersection of Selje-open sets provides a finer approximation  
than the intersection of micro-open or nano-open sets:  
SJR int(AB) Micint(AB) LR(AB)  
Proof: 1. In nano topology,LR(AB) {x U | x LR(A) LR(B)}  
.
.
2. In micro topology,Micint(AB) {x U | x Micint(A) Micint(B)}  
3. In Selje topology, SJR int(AB) {x U | x SJR int(A) SJR int(B)}  
,
thus, providing a finer approximation.  
The below corollary states that Selje Topological Space generalizes both nano  
and micro topologies, but not all Selje-open sets are nano-open or micro-open,  
offering a broader and more flexible structure.  
Corollary: (Generalization of Nano and Micro Topologies). Selje  
Topological Space generalizes both nano and micro topologies. Every nano-  
open and micro-open set is a Selje-open set, but not every Selje-open set is  
nano-open or micro-open.  
Proof: By the definition of Selje Topology, R(U) µR(U) SJR(U)  
,
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
49  
meaning all nano-open and micro-open sets belong to the Selje Topology. However,  
Selje-open sets can contain additional elements that nano and micro topologies  
cannot capture.  
4. Topological Analysis of Climate Change Impact: A Comparative Study Using  
Nano, Micro and Selje Topologies  
This application focuses on differentiating three topological spaces-nano  
topology, micro topology and Selje Topology-through the lens of climate change  
impact analysis. Climate change, a multifactorial process, affects various sectors like  
agriculture, health and the economy, with factors such as temperature rise, rainfall  
patterns and sea level rise influencing different regions in diverse ways.  
By modeling these factors within each topological space, we aim to identify  
which regions and sectors are most affected. The process involves analyzing key  
climate-related variables, applying each topological method to assess their  
significance and comparing the results to determine how each topology captures  
critical factors. The comparison highlights the strengths of each topology, with  
special focus on how Selje Topology refines the relationships between variables,  
offering a more detailed and precise analysis compared to nano and micro topologies.  
In the end, the betterment of each topological space is analyzed, showing how they  
differ in precision, scalability and flexibility in identifying the most impactful factors  
of climate change on different regions.  
4.1 Methodology for Topological Analysis of Climate Change Impact:  
The following structured steps outline the methodology used for applying nano,  
micro and Selje topologies to analyze climate change impacts:  
•
Data Preparation: Collected and standardized climate data, focusing on critical  
factors such as temperature rise, rainfall patterns, sea level rise, greenhouse gas  
emissions, deforestation and other socio-economic variables across various regions  
and sectors. This data was organized to ensure consistency and comparability across  
different regions.  
•
Topological Space Application: Applied nano, micro and Selje Topological  
Spaces to the climate data to assess the relationships between the key factors. The  
topologies were used to study how these factors interact and influence one another in  
various regions, allowing for the identification of underlying patterns in the data.  
Special attention was paid to how the different topological spaces handle these  
relationships, particularly their set approximations and scalability.  
50  
V. JEYANTHI, AND N. SELVA NANDHINI  
•
Critical Factor Identification: Determined the most significant climate-related  
factors for each region by analyzing the topological spaces. The analysis focused on  
identifying which variables-such as temperature rise, rainfall variability, or  
deforestation-had the greatest impact on environmental, economic and health  
outcomes in specific regions.  
•
Visualization and Analysis: Generated diagrams, tables and comparative metrics  
to visualize the relationships between climate factors and the regions they affect.  
These visualizations highlight the differences in performance between nano, micro  
and Selje topologies. (Add visual aids such as graphs comparing factor influence  
across regions for each topology to show how Selje provides deeper insights.)  
•
Comparison of Topologies: Compared the efficiency and flexibility of nano,  
micro and Selje Topologies in analyzing the climate change impact. This comparison  
focused on determining which topology provided the most accurate and scalable  
analysis for multi- factorial climate systems. Results showed that while all three  
topologies identified key variables, Selje topology allowed for more detailed insights  
into variable interactions, offering superior scalability and precision in the analysis of  
complex datasets.  
4.2 Topological Analysis of Climate Change Impact: The table below  
presents the data collected for climate change impact analysis. This data is then  
processed to compare the performance of nano, micro and Selje Topological Spaces.  
Region Temp- Rainfall  
Sea  
Level  
(Sl)  
GHG Defores- Agri. Health  
Eco-  
nomic  
Costs  
(Ec)  
Impact  
Rate(Ir)  
rature  
(Te)  
(Ra)  
tation(D) Prod. Impacts  
(Ap) (Hi)  
Emis-  
sions  
(GHG)  
Coastal  
Regions  
(Cr)  
Medium  
Medium  
Agri  
cultural  
Lands  
(Al)  
Forested  
Areas  
(Fa)  
Urban  
Areas  
(Ua)  
High  
High  
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
51  
Region Temp- Rainfall  
Sea  
Level  
(Sl)  
GHG Defores- Agri. Health  
Eco-  
nomic  
Costs  
Impact  
rature  
(Te)  
(Ra)  
tation(D) Prod. Impacts  
(Ap) (Hi)  
Rate(Ir)  
Medium  
High  
Emis-  
sions  
Island  
Nations  
(In)  
River  
Basins  
(Rb)  
Energy  
Sector  
(Es)  
High  
High  
High  
Fisheries  
(Fs)  
Tourism  
Indus-  
try (Ti)  
Health  
care Sys-  
tems  
Medium  
(Hs)  
Table 1: Impact of Climate Change on Various Regions and Sectors  
Let the set of region be E = {Cr,Al,F,Ua,In,Rb,Es,Fs,Ti,Hs}  
and  
G = {Te,Ra,Sl,GHG,De,Ap,Hi,Ec,Ir}.  
It splits into two cases where  
H = {Te,Ra,Sl,GHG,De,Ap,Hi,Ec} and I = {Ir}  
The group of Equivalence types V/H corresponding to H is given by  
V/H = {{Cr},{Al,In},{Ua},{Fa,Rb,Es},{Ti},{Fs,Hs}},  
E = {Fa,Ua,Rb,Es,Fs,Ti}  
Case 1: When Impact level is High  
52  
V. JEYANTHI, AND N. SELVA NANDHINI  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fs,Hs},{Fa,Ua,Rb,Es,Fs,Ti,Hs}}  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},{Al,Fs,Hs},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Ti},  
{Cr,Al,Fa,In,Es,Ti},{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},  
{Al,Ua,In},{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},  
{Al,Fs,Hs},{Cr,Al,Fa,In,Es,Fs,Hs},{Al,Fa,Es,Fs,Ti,Hs},  
{Ua,Rb,Fs,Hs},{Cr,Fa,Ua,In,Rb,Es,Ti,Hs},{Fa,Ua,Rb,Es,Fs,Ti,Hs}}  
Phase I: Te is removed  
T(E) = {,V,{Fa,Ua,Rb,Es},{Al,Fa,Ua,In,Rb,Es,Fs,Ti,Hs},{Al,In,Fs,Ti,Hs}}  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es},{Al,Fa,Ua,Rb,Es},  
{Al,Fa,Ua,In,Rb,Es,Fs,Ti,Hs}}  
SJH(E) = {,V,{Al},{Al,Fa,Es},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},{Ua,Rb},  
{Fa,Ua,Rb,Es},{Fa,Ua,Rb,Es,Ti},{Cr,Fa,Ua,In,Rb,Es,Ti},{Al,Ua,Rb},  
{Al,Fa,Ua,Rb,Es},{Fa,Es},{Fa,Es,Ti},{Cr,Fa,In,Es,Ti},  
{Al,Ua,Rb,Fs,Hs},{Al,Fa,Ua,Rb,Es,Fs,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},  
{Fa,Es},{Fa,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Cr,Al,Fa,Ua,In,Rb,Es,Ti}}  
Phase II: Ra is removed  
T(E) = {,V, {Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}}  
µ(E) = {,V,{Al},}Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},{Al,Ua,Rb},  
{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}  
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
53  
Phase III: Sl is removed  
T(E) = {,V, {Fa,Rb,Es,Ti},{Cr,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Cr,Ua,Fs,Hs}}  
µ(E) = {,V, {Al},{Fa,Rb,Es,Ti},{Al,Fa,Rb,Es,Ti},{Cr,Fa,Ua,Rb,Es,Fs,Ti,Hs},  
{Cr,Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Cr,Ua,Fs,Hs},{Cr,Al,Ua,Fs,Hs}}  
SJH(E) = {,V,{Al},{Al,Fa},{Al,Fa,Es,Ti},{Cr,Al,Fa,Es,Ti},{Cr,Al},  
{Cr,Al,Fa,In,Es,Ti},{Rb},{Fa,Rb},{Fa,Rb,Es,Ti},{Cr,Fa,Rb,Es,Ti},  
{Al,Rb},{Al,Fa,Rb},{Al,Fa,Rb,Es,Ti},{Cr,Al,Fa,Rb,Es,Ti},  
{Cr,Al,Rb},{Cr,Al,Fa,In,Rb,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Fs,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},  
{Cr,Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Ua,Fs,Hs},{Fa,Ua,Fs,Hs},  
{Fa,Ua,Es,Fs,Hs},{Cr,Fa,Ua,Es,Fs,Ti,Hs},{Cr,Ua,Fs,Hs},  
{Cr,Fa,Ua,In,Es,Fs,Ti,Hs},{Al,Ua,Fs,Hs}{Al,Fa,Ua,Fs,Hs}  
{Al,Fa,Ua,Es,Fs,Ti,Hs},{Cr,Al,Fa,Ua,Es,Fs,Ti,Hs},{Cr,Al,Ua,Fs,Hs},  
{Cr,Al,Fa,Ua,In,Es,Fs,Ti,Hs},{Fa},{Fa,Es,Ti},{Cr,Fa,Es,Ti},{Cr},  
{Cr,Fa,In,Es,Ti},{Cr,Al,Ua,Rb,Fs,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs}}  
Phase IV: GHG is removed  
T(E) = {,V,{Fa,Rb,Es,Ti},{Fa,Ua,In,Rb,Es,Fs,Ti,Hs},{Fa,Ua,Rb,Fs,Hs}}  
µ(E) = {,V,{Al},{Fa,Rb,Es,Ti},{Al,Fa,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},  
{Al,Fa,Rb,Es,Fs,Ti,Hs},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Hs}}  
SJH(E) = {,V, {Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Fa,Es},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},  
{Cr,Al,Fa,In,Es,Ti},{Al,Fa,Es,Ti},{Al,Fa,Es},{Rb},{Cr,Fa,In,Rb,Es,Ti},  
{Fa,Rb,Es,Ti},{Fa,Rb,Es},{Al,Rb},{Cr,Al,Fa,In,Rb,Es,Ti},  
{Al,Fa,Rb,Es,Ti},{Al,Fa,Rb,Es},{Ua,Rb,Fs,Hs},  
{Cr,Al,Fa,In,Rb,Es,Fs,Ti,Hs},{Al,Fa,Rb,Es,Fs,Ti,Hs},  
{Al,Fa,Rb,Es,Fs,Hs}}  
Phase V: De is removed  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}}  
54  
V. JEYANTHI, AND N. SELVA NANDHINI  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},{Al,Ua,Rb},  
{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}}  
Phase VI: Ap is removed  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}}  
µ(E) ={,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V, {Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},{Al,Ua,Rb},  
{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}}  
Phase VII: Hi is removed  
T(E) = {,V,{Fa,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Ua,Fs,Hs}}  
µ(E) = {,V,{Al},{Fa,Rb,Es,Ti},{Al,Fa,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Ua,Fs,Hs},{Al,Ua,Fs,Hs}}  
SJH(E) = {,V,{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},{Rb},{Fa,Rb,Es,Ti},  
{Cr,Fa,In,Rb,Es,Ti},{Al,Rb},{Al,Fa,Rb,Es,Ti},Cr,Al,Fa,Ua,In,Rb,Es,Ti},  
{Ua,Rb,Fs,Hs},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Cr,Fa,Ua,In,Rb,Es,Fs,Ti,Hs},  
{Al,Ua,Rb,Fs,Hs},{Al,Fa,Ua,Es,Fs,Ti,Hs},{Cr,Al,Fa,Ua,In,Es,Fs,Ti,Hs},  
{Fa,Es,Ti},{Cr,Fa,In,Es,Ti}}  
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
55  
Phase VIII: Ec is removed  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}}  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},{Al,Ua,Rb},  
{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}}  
Following the aforementioned analysis of CrRase Cr, it has been determined  
that the principal factors affecting climate change impact are Rainfall, Deforestation,  
Algricultural Productivity and Economic Crosts.  
Case 2: When Impact level is Normal  
T(E) = {,V,{Cr,Al,In},{Cr,Al,In,Fs,Hs},{Fs,Hs}}  
µ(E) = {,V,{Al},{Cr,Al,In},{Cr,Al,In,Fs,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Al},{Cr,Al},{Cr,Al,In,Ti},{Cr,Al,Fa,In,Es,Ti},{Al,Fs,Hs},  
{Cr,Al,Fs,Hs},{Cr,Al,In,Fs,Ti,Hs},{Cr,Al,Fa,In,Es,Fs,Ti,Hs},  
{Fs,Hs},{Cr,Fs,Hs},{Cr,In,Fs,Ti,Hs},{Cr,Fa,In,Es,Fs,Ti,Hs},  
{Cr},{Cr,In,Ti},{Cr,Fa,In,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Cr,Al,Ua,Rb,Fs,Hs},{Cr,Al,Ua,In,Rb,Fs,Ti,Hs}}  
Phase I: Te is removed  
T(E) = {,V,{Cr},{Cr,Al,In,Fs,Ti,Hs},{Al,In,Fs,Ti,Hs}  
µ(E) = {,V,{Al},{Cr},{Cr,Al},{Cr,Al,In,Fs,Ti,Hs},{Al,In,Fs,Ti,Hs}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Cr},{Cr,In,Ti},{In,Ti},{Al,Ua,Rb,Fs,Hs},  
56  
V. JEYANTHI, AND N. SELVA NANDHINI  
{Cr,Al,Ua,Rb,Fs,Hs},{Cr,Al,Ua,In,Rb,Fs,Ti,Hs},  
{Al,Ua,In,Rb,Fs,Ti,Hs},{Al},{Cr,Al,Fa,In,Es,Ti},{Cr,Al},{Cr,Al,In,Ti},  
{Al,In,Ti},{Al,Fs,Hs} {Cr,Al,Fa,In,Es,Fs,Ti,Hs},{Cr,Al,In,Fs,Ti,Hs},  
{Al,In,Fs,Ti,Hs},{Cr,Al,Fs,Hs}}  
Phase II: Ra is removed  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},  
{Al,Ua,Rb},{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fs,Hs},{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}}  
Phase III: Sl is removed  
T(E) = {,V,{Al,In}{Cr,Ua,Fs,Hs},{Cr,Al,Ua,In,Fs,Hs}}  
µ(E) ={,V,{Al},{Al,In},{Cr,UaFs,Hs},{Cr,Al,Ua,Fs,Hs},{Cr,Al,Ua,In,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Cr},{In},{Cr,In},{Al,Ua,Rb,Fs,Hs},  
{Al,Ua,In,Rb,Fs,Hs},{Cr,Al,Ua,Rb,Fs,Hs},{Cr,Al,Ua,In,Rb,Fs,Hs},  
{Al},{Cr,Al,Fa,In,Es,Ti},{Al,In},{Cr,Al},{Cr,Al,In},{Ua,FsHs},  
{Cr,Fa,Ua,In,Es,Fs,Ti,Hs},{Ua,In,Fs,Hs},{Cr,Ua,Fs,Hs},  
{Cr,Ua,In,Fs,Hs},{Al,Ua,Fs,Hs},{Cr,Al,Fa,Ua,In,Es,Fs,Ti,Hs},  
{Al,Ua,In,Fs,Hs},{Cr,Al,Ua,Fs,Hs},{Cr,Al,Ua,In,Fs,Hs}}  
Phase IV: GHG is removed  
T(E) = {,V,{Cr,Al,In},{Fa,Rb,Es,Fs,Hs},{Cr,Al,Fa,In,Rb,Es,Fs,Ti,Hs}}  
µ(E) = {,V,{Al},{Cr,Al,In},{Fa,Rb,Es,Fs,Hs},{Al,Fa,Rb,Es,Fs,Hs},  
{Cr,Al,Fa,In,Rb,Es,Fs,Hs}}  
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
57  
SJH(E) = {,V,{Al},{Cr,Al,In},{Al,Fa,Es},{Al,Fa,In,Es},{Cr,Al,Fa,In,Es,Ti},  
{Rb,Fs,Hs},{Cr,In,Rb,Fs,Hs},{Fa,Rb,Es,Fs,Hs},{Fa,In,Rb,Fs,Hs},  
{Cr,Fa,In,Rb,Es,Fs,Ti,Hs},{Al,Rb,Fs,Hs},{Cr,Al,In,Rb,Fs,Ti,Hs},  
{Al,Fa,Rb,Es,Fs,Hs},{Al,Fa,In,Rb,Es,Fs,Hs},  
{Cr,Al,Fa,In,Rb,Es,Fs,Ti,Hs},{Cr,In},{Fa,In},{Fa,In,Ti},  
{Cr,Fa,In,Es,Ti},{Al,Ua,Rb,Fs,Hs},{Cr,Al,Ua,Fs,Rb,Fs,Hs},  
{Al,Fa,Rb,Es,Fs,Hs},{Al,Fa,In,Rb,Es,Fs,Hs}}  
Phase V: De is removed  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},{Al,Ua,Rb},  
{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}}  
Phase VI: Ap is removed  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}}  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},  
{Al,Ua,Rb},{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}}  
Phase VII: Hi is removed  
58  
V. JEYANTHI, AND N. SELVA NANDHINI  
T(E) = {,V,{Cr,Al,In},{Cr,Al,Ua,In,Fs,Hs},{Ua,Fs,Hs}}  
µ(E) ={,V,{Al},{Cr,Al,In},{Cr,Al,Ua,In,Fs,Hs},{Ua,Fs,Hs},{Al,Ua,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Cr},{Cr,In},{Al,Ua,Rb,Fs,Hs},  
{Cr,Al,Ua,Rb,Fs,Hs},{Cr,Al,Ua,In,Rb,Fs,Hs},{Al},{Cr,Al,Fa,In,Es,Ti},  
{Cr,Al},{Cr,Al,In},{Al,Ua,Fs,Hs},{Cr,Al,Fa,Ua,In,Es,Fs,Ti,Hs},  
{Cr,Al,Ua,Fs,Hs},{Cr,Al,Ua,In,Fs,Hs},  
{Ua,Fs,Hs},{Cr,Fa,Ua,In,Es,Fs,Ti,Hs},{Cr,Ua,Fs,Hs},  
{Cr,Ua,In,Fs,Hs}}  
Phase VIII: Ec is removed  
T(E) = {,V,{Fa,Ua,Rb,Es,Ti},{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs}}  
µ(E) = {,V,{Al},{Fa,Ua,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},  
{Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Fs,Hs},{Al,Fs,Hs}}  
SJH(E) = {,V,{Cr,Fa,In,Es,Ti},{Fa,Es,Ti},{Al,Ua,Rb,Fs,Hs},  
{Al,Fa,Ua,Rb,Es,Fs,Ti,Hs},{Al},{Al,Fa,Es,Ti},{Cr,Al,Fa,In,Es,Ti},  
{Ua,Rb},{Cr,Fa,Ua,In,Rb,Es,Ti},{Fa,Ua,Rb,Es,Ti},{Al,Ua,Rb},  
{Cr,Al,Fa,Ua,In,Rb,Es,Ti},{Al,Fa,Ua,Rb,Es,Ti},{Fs,Hs},  
{Cr,Fa,In,Es,Fs,Ti,Hs},{Fa,Es,Fs,Ti,Hs},{Al,Fs,Hs},  
{Cr,Al,Fa,In,Es,Fs,Ti,Hs}}  
From both Case 1 and Case 2, it is clear that Rainfall, Deforestation,  
Agricultural Productivity and Economic Costs play a crucial role in driving climate  
change outcomes.  
Visualization and Analysis  
To provide a clear comparison of the performance of nano, micro and Selje  
topologies in identifying critical climate factors, a heat map was generated (see  
Figure 1). This visual repre- sentation compares the ability of each topology to detect  
key factors, such as temperature rise, rainfall variability and deforestation, across  
various regions including Coastal, Agricultural, Urban, Forested and Island regions.  
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
59  
Figure 1: Heat Map of Topology Performance by Region  
The heat map shows the performance score of each topology, with darker shades  
representing better performance in terms of accurately identifying impactful factors.  
As seen in the heat map, the Selje topology consistently demonstrates superior  
performance across all regions, particularly in complex environments like urban and  
forested areas, where multifactorial dependencies are prevalent.  
5. Results and Discussion  
Comparison of Nano, Micro and Selje Topological Spaces  
In this analysis, nano topology, micro topology and Selje topology were  
applied to climate change impact factors to assess their efficiency in identifying  
critical variables. While all three topologies consistently identified Rainfall,  
Deforestation, Agricultural Productivity and Economic Costs as major factors, the  
depth of analysis, precision and flexibility differed significantly across the topologies.  
Nano Topology  
Strengths: Nano topology provides a simple binary classification of critical  
climate factors, making it effective for identifying whether a factor is part of a critical  
set.  
60  
V. JEYANTHI, AND N. SELVA NANDHINI  
Weaknesses: Its binary approach cannot capture the complexities of  
dynamic systems, leading to limitations in handling multifactorial relationships,  
scalability and interdependencies.  
Micro Topology  
Strengths: Micro topology refines nano topology by introducing micro-open  
and micro closed sets, allowing for more nuanced classifications and adaptable  
relationships between factors.  
Weaknesses: While an improvement, micro topology still struggles with  
highly multifactorial systems, lacking the precision needed to fully address the  
complex, interconnected nature of climate factors.  
Selje Topology  
Strengths: Selje topology generalizes both nano and micro topologies,  
providing superior flexibility and precision. It uses Selje-open and Selje-closed sets  
to capture intricate relationships between climate factors, even in dynamic and  
multifactorial systems.  
Theorem 1: Demonstrates finer approximations through better handling of  
closures and interiors.  
Theorem 2: Highlights Selje’s superior scalability, enabling it to handle  
complex systems more effectively.  
Theorem 3: Proves Selje topology’s ability to capture interdependencies  
through finer approximations of set intersections.  
Better Performance: Selje topology offers deeper insights into the  
variability of climate impacts across regions. Unlike nano and micro, which treat  
factors as static, Selje allows for a dynamic understanding of how these factors  
fluctuate under different conditions and regions.  
Weaknesses: The complexity of Selje topology may be unnecessary for  
simpler systems where its precision is not required.  
Selje Topology’s Superiority  
While all three topologies identified the same major factors, Selje topology  
stands out due to its enhanced precision, scalability and ability to capture complex  
relationships.  
A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
61  
Precision in Complex Systems: It handles intricate, multifactorial  
environments like climate change, providing a finer analysis of the interactions  
between key factors.  
Scalability: As demonstrated in Theorem 3.3, Selje topology scales well with  
system complexity, retaining accuracy even as more variables are introduced.  
Handling Nuanced Relationships: Theorem 3.4 shows that Selje topology  
excels in analyzing overlapping and interdependent factors, offering a more detailed  
understanding of cumulative impacts.  
Flexibility: Unlike nano’s rigid binary classification, Selje topology adapts to  
uncertainties and changing conditions, making it more versatile for dynamic systems.  
6. Conclusion  
While nano, micro and Selje topologies all identified the same key climate  
factors, Selje topology offers greater analytical power due to its flexibility, precision  
and scalability. These qualities make it the optimal choice for analyzing complex,  
multifactorial systems like climate change, where relationships between factors are  
dynamic and interdependent. Future research could explore Selje topology’s  
application in other fields, such as optimizing smart grids or analyzing healthcare  
systems, where multifactorial interactions are critical. Its adaptability and precision  
make it well-suited for real-world applications in dynamic environments, providing  
deeper insights and better handling of complex systems.  
Conflict of Interest  
The authors affirm that there is no conflicts of interest pertaining to the  
research presented in this paper. No financial or personal relationships with any  
organizations or individuals that could potentially bias the findings or interpretations  
are reported.  
Acknowledgment  
Authors would like to express their gratitude to everyone who supported us  
throughout this independent research. Without external funding, this work is a result  
of our own dedication and perseverance. Authors are also thankful for the insightful  
feedback from our peers, which greatly enriched this study.  
62  
V. JEYANTHI, AND N. SELVA NANDHINI  
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A COMPARATIVE ANALYSIS OF SELJE TOPOLOGICAL SPACE  
63  
1. Assistant Professor,  
2. Research Scholar  
(Received, November 15, 2024)  
(Revised, November 19, 2024)  
Department of Mathematics,  
Sri Krishna Arts and Science College,  
Kuniamuthur, Coimbatore, TamilNadu, India-641008.  
1. E-mail: jeyanthivenkatapathy@gmail.com,  
2. E-mail: nandhininagaraj230@gmail.com