On Subgroups of Topologized Fundamental Groups and Generalized Coverings

TL;DR

This paper explores the relationships between subgroups of topologized fundamental groups and generalized covering maps, establishing conditions for their equivalence and analyzing their topological properties.

Contribution

It introduces new conditions under which generalized coverings, semicoverings, and coverings coincide, and examines the influence of subgroup topologies on covering structures.

Findings

Identifies relationships between generalized covering subgroups and classical subgroups

Provides conditions for the equivalence of generalized coverings, semicoverings, and coverings

Analyzes the impact of topologies on fundamental groups on covering properties

Abstract

In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology. Moreover, we present some conditions under which generalized coverings, semicoverings and coverings are equal.