A Critical Study of Compactness Properties Of Topological Groups
Author(s): Dr. Satish Raj
Publication #: 2504009
Date of Publication: 07.04.2025
Country: India
Pages: 1-4
Published In: Volume 11 Issue 2 April-2025
Abstract
Topological groups is logically the combination of groups and topological spaces, they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures together and consequently they are not independent from each other. The generalised structure which includes several fields such point set topology, algebraic topology, and differential topology. Dubois, D(5), J. Zhang(10), Felix Hausdorff, Maurice Frechet, and Henri Poincare studied its basic properties based on Topological space and some geometrical structure. A pre-topological group G is a group which is also a pre-topological space such that the multiplication mapping of G × G into G sending x × y into x • y, and the inverse mapping of H into G sending x into x−1, are pre-continuous mappings.
Keywords: Topological Groups, Euclidean Topology, Hausdorff, Algebraic Topology, Arbitrary Unions And Homeomorphism
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