Geodesic
An equivalent condition for a pseudo (k0 , k 1 )-covering space
Filomat, Tome 36 (2022) no. 15, p. 5093

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DOI

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 digital-topological imbedding 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.
DOI : 10.2298/FIL2215093H
Classification : 54C08, 68R10, 05C40
Keywords: Pseudo-local (k0, k1)-isomorphism, weakly local (k0, k1)-isomorphism, digital-topological imbedding, embedding, pseudo-covering, unique pseudo-lifting property 
Sang-Eon Han. An equivalent condition for a pseudo (k0 , k 1 )-covering space. Filomat, Tome 36 (2022) no. 15, p. 5093 . doi: 10.2298/FIL2215093H
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     author = {Sang-Eon Han},
     title = {An equivalent condition for a pseudo (k0 , k 1 )-covering space},
     journal = {Filomat},
     pages = {5093 },
     year = {2022},
     volume = {36},
     number = {15},
     doi = {10.2298/FIL2215093H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2215093H/}
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