Topological groups that realize homogeneity of topological spaces

TL;DR

This paper investigates how to simplify acting groups in topological spaces while maintaining properties like transitivity and coset structure, contributing to the understanding of symmetry and homogeneity in topology.

Contribution

It introduces methods to simplify acting groups that preserve key properties such as transitivity and coset structures in topological spaces.

Findings

Simplification techniques for acting groups preserving transitivity.

Conditions under which a group action maintains coset space structure.

Results on preserving equiuniformities in G-Tychonoff spaces.

Abstract

We present results on simplifying an acting group preserving properties of actions: transitivity, being a coset space and preserving a fixed equiuniformity in case of a $G$-Tychonoff space.