Developing a topology generator using Python program

In the research domain of Mathematics, Topology plays a major role as it is all about studying the surfaces or the region. It deals with the objects that retain their properties irrespective of continuously changing their shape but without adding any additional substance over them or without making...

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Bibliographic Details
Main Authors: Prabu, M. Vivek, Rahini, M.
Format: Conference Proceeding
Language:English
Subjects:
Axioms
Topology
Online Access:Get full text
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Summary:In the research domain of Mathematics, Topology plays a major role as it is all about studying the surfaces or the region. It deals with the objects that retain their properties irrespective of continuously changing their shape but without adding any additional substance over them or without making any additional hole in them. In point set topology, for any set, if some of its subsets are collected in such a way that it possesses three specific conditions, then such a collection will be known as the topology for that set. Though it sounds simple, practically it turns hectic to frame such collections when the cardinality (n) of the set is large. For instance, for any set with n=3, one can frame 29 distinct topologies. But all of a sudden, when n=4, the total number of possible topologies raise to 355. Thus, arriving at such a collection with more subsets satisfying the topological axioms turns highly complicated. To overcome this issue, in this paper, we have developed a Python program which will act as the Topology Generator. Irrespective of the cardinality of the set, this coding will function effectively such that as and when the topologists are in need of making use of a topology with a larger number of subsets in it, it won’t be hectic any more. In that way, this program might be helpful for larger range of audience starting from the students who are undergoing their masters up to the eminent researchers in the field of topology.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0114732