IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i11p1072-d284750.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/11/1072/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/11/1072/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sang-Eon Han, 2021. "Discrete Group Actions on Digital Objects and Fixed Point Sets by Iso k (·)-Actions," Mathematics, MDPI, vol. 9(3), pages 1-25, February.
    2. Sang-Eon Han, 2020. "Digital k -Contractibility of an n -Times Iterated Connected Sum of Simple Closed k -Surfaces and Almost Fixed Point Property," Mathematics, MDPI, vol. 8(3), pages 1-23, March.
    3. Sang-Eon Han, 2019. "Fixed Point Theory for Digital k -Surfaces and Some Remarks on the Euler Characteristics of Digital Closed Surfaces," Mathematics, MDPI, vol. 7(12), pages 1-19, December.
    4. Sang-Eon Han, 2019. "Links between Contractibility and Fixed Point Property for Khalimsky Topological Spaces," Mathematics, MDPI, vol. 8(1), pages 1-16, December.
    5. Sang-Eon Han & Selma Özçağ, 2020. "The Fixed Point Property of the Infinite M -Sphere," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    6. Sang-Eon Han, 2020. "Digital Topological Properties of an Alignment of Fixed Point Sets," Mathematics, MDPI, vol. 8(6), pages 1-18, June.
    7. 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.
    8. Sang-Eon Han, 2020. "Fixed Point Sets of k -Continuous Self-Maps of m -Iterated Digital Wedges," Mathematics, MDPI, vol. 8(9), pages 1-26, September.
    9. Sang-Eon Han, 2020. "Fixed Point Sets of Digital Curves and Digital Surfaces," Mathematics, MDPI, vol. 8(11), pages 1-25, October.
    10. Sang-Eon Han, 2020. "The Most Refined Axiom for a Digital Covering Space and Its Utilities," Mathematics, MDPI, vol. 8(11), pages 1-21, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1072-:d:284750. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.