Equivalent Conditions for Digital Covering Maps

TL;DR

This paper characterizes digital covering maps through local isomorphisms, provides a loop criterion for n-radius coverings, and discusses conditions under which maps with unique path lifting are covering maps.

Contribution

It establishes equivalent conditions for digital covering maps, introduces a loop criterion for n-radius coverings, and clarifies when maps with unique path lifting are coverings.

Findings

Digital covering maps are equivalent to local isomorphisms.

A loop criterion for n-radius digital coverings is provided.

Maps with unique path lifting and no conciliator point are covering maps.

Abstract

In this paper we show that a digital $(\kappa,\lambda)-$continuous surjection $p:(E,\kappa)\rightarrow (B,\lambda)$ is a digital covering map if and only if it is a local isomorphism. Moreover, we find a loop criterion for a digital covering map to be an $n$-radius covering. Also, we show that every digitally continuous map with unique path lifting property is a digital covering map if it has no conciliator point.