Remarks on topological spaces on $ {\mathbb Z}^n $ which are related to the Khalimsky $ n $-dimensional space

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2021Publisher:American Institute of Mathematical Sciences (AIMS)Journal:AIMS Mathematics, volume 7, pages 1,224-1,240 (issn: 2473-6988,

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Authors: Sang-Eon Han; Saeid Jafari; Jeong Min Kang; Sik Lee;

doi: 10.3934/math.2022072

Remarks on topological spaces on $ {\mathbb Z}^n $ which are related to the Khalimsky $ n $-dimensional space

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Abstract

<abstract><p>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.</p></abstract>

Related Organizations

Jeonbuk National University
Korea (Republic of)
University of Seoul
Korea (Republic of)
Chonnam National University
Korea (Republic of)
HF & VUC Klar
Denmark

Keywords

digital topology, alexandroff topology, t<sub>&#189</sub>-separation axiom, QA1-939, quasi-discrete, khalimsky topology, Mathematics

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