The maximal G-compactifications of G-spaces with special actions

TL;DR

This paper investigates conditions under which the maximal G-compactification of a G-space can be realized as a completion of the phase space, and explores the structure of G-spaces with special actions.

Contribution

It provides criteria for obtaining the maximal G-compactification via uniformities and analyzes the structure of G-spaces with particular types of actions.

Findings

Maximal G-compactification can be achieved through specific uniformities.

Characterization of G-spaces with special actions.

Structural insights into G-spaces based on their actions.

Abstract

An action on a G-space induces uniformities on the phase space. It is shown when the maximal G-compactification of a G-space can be obtained as a completion of the phase space with respect to one of these uniformities. Structure of G-spaces with special actions is investigated.