Remarks on pseudocovering spaces in a digital topological setting

Abstract

After investigating some properties of the original version of a pseudo-$(k_0,k_1)$-covering space in the literature,
it appears that a pseudo-$(k_0,k_1)$-covering space is equivalent to a digital $(k_0,k_1)$-covering space.
Hence, as a corrigendum to \cite{H6,H8},
the paper first revises one of the three conditions for a pseudo-$(k_0,k_1)$-covering space, which broadens the original version.
After that, we suggest some examples for the revised version of a pseudo-$(k_0,k_1)$-covering map.
Since the revised map is so related to the study of several kinds of path liftings, this new version can facilitate some studies in the field of applied topology including digital topology.
We note that a weakly local $(k_0,k_1)$-isomorphic surjection is equivalent to the new version of a pseudo-$(k_0,k_1)$-map instead of the original version of a pseudo-$(k_0,k_1)$-map.
The present paper only deals with $k$-connected digital images $(X, k)$.