When Is a Local Homeomorphism a Semicovering map?

TL;DR

This paper investigates conditions that determine when a local homeomorphism qualifies as a semicovering map or a covering map, enhancing understanding of their relationships in topological spaces.

Contribution

It provides new criteria for identifying when local homeomorphisms are semicovering or covering maps, expanding theoretical knowledge in topology.

Findings

Identifies conditions under which a local homeomorphism is a semicovering map.

Establishes criteria for when a local homeomorphism is a covering map.

Clarifies the relationship between local homeomorphisms, semicovering maps, and covering maps.

Abstract

In this paper, by reviewing the concept of semicovering maps, we present some conditions under which a local homeomorphism becomes a semicovering map. We also obtain some conditions under which a local homeomorphism is a covering map.