Abstract: In this article we study topological groups and their separation axioms. The theory of topological groups is rich in terms of its own profound results and also in terms of its application. We study topological groups mainly to illustrate how the introduction of an algebraic structure on a space affects and enriches its topological properties. As the name implies, a topological group is a topological space whose underlying set is also endowed with a group structure. A topological group is a mathematical object with both an algebraic structure and topological structure. Topological group along with continuous group action are used to study continuous symmetries which have many applications.
Keywords: Filter base, interior of a set, Neighborhood system, semi topological group, separation axioms, and topological group.
Title: A Study on Topological Groups and Their Separation Axioms
Author: Swatilekha Nag
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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