An equivalent condition for a pseudo (k0, k1)-covering space

Abstract

The paper aims at developing the most simplified axiom for a pseudo (k0, k1)-covering space. To make this a success, we need to strongly investigate some properties of a weakly local (WL-, for short) (k0, k1)-isomorphism. More precisely, we initially prove that a digital-topological imbedding w.r.t. a (k0, k1)- isomorphism implies a WL-(k0, k1)-isomorphism. Besides, while a WL-(k0, k1)-isomorphism is proved to be a (k0, k1)-continuous map, it need not be a surjection. However, the converse does not hold. Taking this approach, we prove that aWL-(k0, k1)-isomorphic surjection is equivalent to a pseudo-(k0, k1)-covering map, which simplifies the earlier axiom for a pseudo (k0, k1)-covering space by using one condition. Finally, we further explore some properties of a pseudo (k0, k1)-covering space regarding lifting properties. The present paper only deals with k-connected digital images.