Generalized uniform covering maps relative to subgroups

TL;DR

This paper extends the theory of generalized uniform covering maps by exploring their existence relative to subgroups of the uniform fundamental group, building on prior work in uniform space coverings.

Contribution

It introduces conditions for the existence of covering maps relative to subgroups, advancing the understanding of uniform coverings in the context of subgroup relations.

Findings

Conditions for existence of relative covering maps established

Extension of universal covering map theory to subgroup contexts

Enhanced understanding of uniform fundamental groups

Abstract

In "Rips complexes and covers in the uniform category" \cite{Rips} the authors define, following James \cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given. This paper extends these results by investigating the existence of these covering maps relative to subgroups of the uniform fundamental group and the fundamental group of the base space.