Equivalent Conditions for Digital Covering Maps

Abstract

‎It is known that every digital covering map $p:(E,\kappa)\rightarrow (B,\lambda)$ has uniqe path lifting property‎. ‎In this paper‎, ‎we show that its inverse is true when the continuous surjection map $p$ has no conciliator point‎. ‎Also‎, ‎we prove 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 out a loop criterion for a digital covering map to be a radius ‎$n‎$‎‎ covering‎ ‎map