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Research Article | Open Access

Remarks on topological spaces on Z n which are related to the Khalimsky n-dimensional space

Sang-Eon Han1, Saeid Jafari2, Jeong Min Kang3, Sik Lee4( )
Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju-City Jeonbuk 54896, Republic of Korea
College of Vestsjaelland South, Herrestraede 11 and Mathematical and Physical Science Foundation, 4200 Slagelse, Denmark
Mathematics, School of Liberal, Arts Education, University of Seoul, Seoul 02504, Republic of Korea
Department of Mathematics Education, Chonnam National University, Gwangju-City 61186, Republic of Korea
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Abstract

The present paper intensively studies various properties of certain topologies on the set of integers Z (resp. 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.

Keywords

Khalimsky topologyT1/2-separation axiomAlexandroff topologyquasi-discretedigital topology
CLC number: 54A05, 54J05, 54F05, 54C08, 54F65, 68U05

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 1224-1240
DOI: 10.3934/math.2022072

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Cite this article:
Han S-E, Jafari S, Kang JM, et al. Remarks on topological spaces on Z n which are related to the Khalimsky n-dimensional space. AIMS Mathematics, 2022, 7(1): 1224-1240. https://doi.org/10.3934/math.2022072

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Received: 03 August 2021
Accepted: 30 September 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)