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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Sang-Eon Han & Saeid Jafari & Jeong Min Kang, 2019. "Topologies on Z n that Are Not Homeomorphic to the n -Dimensional Khalimsky Topological Space," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1072-:d:284750
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    References listed on IDEAS

    as
    1. Han, Sang-Eon, 2019. "Estimation of the complexity of a digital image from the viewpoint of fixed point theory," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 236-248.
    2. Jeong Min Kang & Sang-Eon Han & Sik Lee, 2019. "The Fixed Point Property of Non-Retractable Topological Spaces," Mathematics, MDPI, vol. 7(10), pages 1-12, September.
    3. Sang-Eon Han, 2019. "Remarks on the Preservation of the Almost Fixed Point Property Involving Several Types of Digitizations," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    Full references (including those not matched with items on IDEAS)

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