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

AIMS Mathematics

Sang-Eon Han¹  Saeid Jafari²  Jeong Min Kang³  Sik Lee⁴ 

[1] 1. Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju-City Jeonbuk 54896, Republic of Korea;2. College of Vestsjaelland South, Herrestraede 11 and Mathematical and Physical Science Foundation, 4200 Slagelse, Denmark;3. Mathematics, School of Liberal, Arts Education, University of Seoul, Seoul 02504, Republic of Korea;4. Department of Mathematics Education, Chonnam National University, Gwangju-City 61186, Republic of Korea;

关键词: khalimsky topology;    t_½-separation axiom;    alexandroff topology;    quasi-discrete;    digital topology;   

DOI  :  10.3934/math.2022072

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown