Actions of semitopological groups

TL;DR

This paper explores how semitopological and topological groups act continuously and separately continuously on spaces, shedding light on their dynamic properties and potential applications.

Contribution

It provides new insights into the actions of semitopological groups and the distinctions between continuous and separately continuous actions.

Findings

Characterization of continuous transitive actions

Analysis of separately continuous actions of topological groups

Identification of conditions for transitivity in group actions

Abstract

We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.