The present paper intensively studies various properties of certain topologies on the set of integers $ {\mathbb Z} $ (resp. $ {\mathbb Z}^n $) which are either homeomorphic or not homeomorphic to the typical Khalimsky line topology (resp. $ n $-dimensional Khalimsky topology). This finding plays a crucial role in addressing some problems which remain open in the field of digital topology.
Citation: Sang-Eon Han, Saeid Jafari, Jeong Min Kang, Sik Lee. Remarks on topological spaces on $ {\mathbb Z}^n $ which are related to the Khalimsky $ n $-dimensional space[J]. AIMS Mathematics, 2022, 7(1): 1224-1240. doi: 10.3934/math.2022072
The present paper intensively studies various properties of certain topologies on the set of integers $ {\mathbb Z} $ (resp. $ {\mathbb Z}^n $) which are either homeomorphic or not homeomorphic to the typical Khalimsky line topology (resp. $ n $-dimensional Khalimsky topology). This finding plays a crucial role in addressing some problems which remain open in the field of digital topology.
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Sang-Eon Han, Saeid Jafari, Jeong Min Kang, Sik Lee. Remarks on topological spaces on $ {\mathbb Z}^n $ which are related to the Khalimsky $ n $-dimensional space[J]. AIMS Mathematics, 2022, 7(1): 1224-1240. doi: 10.3934/math.2022072
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