AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (374.3 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

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

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
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

9

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
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)