Topologies on Z n that Are Not Homeomorphic to the n -Dimensional Khalimsky Topological Space

Sang-Eon Han, Saeid Jafari and Jeong Min Kang
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Sang-Eon Han: Department of Mathematics Education, Institute of Pure and Applied Mathematics Jeonbuk National University, Jeonju-City 54896, Jeonbuk, Korea
Saeid Jafari: College of Vestsjaelland South Herrestraede 114200 Slagelse, Denmark
Jeong Min Kang: Mathematics, School of Liberal, Arts Education, University of Seoul, Seoul 02504, Korea

Mathematics, 2019, vol. 7, issue 11, 1-12

Abstract: The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ? N , we develop countably many topologies on Z n which are not homeomorphic to the typical n -dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

Keywords: khalimsky topology; quasi-discrete (clopen or pseudo-discrete); T 1 2 -separation axiom; alexandroff topology; digital topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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