On Semicovering, Subsemicovering and Subcovering Maps

TL;DR

This paper extends the concept of subcovering maps to subsemicovering maps, providing conditions for local homeomorphisms to be subsemicoverings and characterizing when they are semicoverings.

Contribution

It introduces the notion of subsemicovering maps, expanding the theory of covering maps with new conditions and relationships.

Findings

Necessary and sufficient conditions for local homeomorphisms to be subsemicoverings.

Examples illustrating the relationship between conditions.

A characterization of when a subsemicovering map is semicovering.

Abstract

In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a subsemicovering map. Moreover, we investigate the relationship between these conditions by some examples. Finally, we give a necessary and sufficient condition for a subsemicovering map to be semicovering.