Yu. M. Smirnov's General Equivariant Shape Theory

TL;DR

This paper develops a comprehensive equivariant shape theory for arbitrary G-spaces with compact groups, utilizing pseudometric methods introduced by Smirnov in 1985, advancing the understanding of topological group actions.

Contribution

It introduces a general equivariant shape theory for G-spaces using pseudometric techniques, extending prior approaches to broader classes of spaces and group actions.

Findings

Constructed a new equivariant shape theory for G-spaces.

Applied pseudometric methods to analyze topological group actions.

Extended Smirnov's earlier methods to more general settings.

Abstract

A general equivariant shape theory for arbitrary $G$-spaces in the case of a compact group $G$ is constructed by using the method of pseudometrics suggested by Yu. M. Smirnov as early as in 1985 at the fifth Tiraspol symposium on general topology and its applications.