An equivalent condition for a pseudo $(k_0, k_1)$-covering space

Sang-Eon Han


The paper aims at developing the most simplified axiom for a pseudo $(k_0, k_1)$-covering space.
 To make this a success, we need to strongly investigate some properties of a weakly local ($WL$-, for short) $(k_0, k_1)$-isomorphism.
 More precisely, we initially prove that a digitally topological imbedding {\it w.r.t.} a $(k_0, k_1)$-isomorphism implies a $WL$-$(k_0, k_1)$-isomorphism.
 Besides, while a $WL$-$(k_0, k_1)$-isomorphism is proved to be a $(k_0, k_1)$-continuous map, it need not be a surjection. However, the converse does not hold.
 Taking this approach, we prove that a $WL$-$(k_0, k_1)$-isomorphic surjection is equivalent to a pseudo-$(k_0, k_1)$-covering map, which simplifies the earlier axiom for a pseudo $(k_0, k_1)$-covering space by using one condition.
Finally, we further explore some properties of a pseudo $(k_0, k_1)$-covering space regarding lifting properties.
The present paper only deals with $k$-connected digital images.


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