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The Fixed Point Property of Non-Retractable Topological Spaces

Author

Listed:
  • Jeong Min Kang

    (Mathematics, School of Liberal, Arts Education, University of Seoul, Seoul 02504, Korea)

  • Sang-Eon Han

    (Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk 54896, Korea)

  • Sik Lee

    (Department of Mathematics Education, Chonnam National University, Gwangju 500-757, Korea)

Abstract

Unlike the study of the fixed point property ( FPP , for brevity) of retractable topological spaces, the research of the FPP of non-retractable topological spaces remains. The present paper deals with the issue. Based on order-theoretic foundations and fixed point theory for Khalimsky ( K -, for short) topological spaces, the present paper studies the product property of the FPP for K -topological spaces. Furthermore, the paper investigates the FPP of various types of connected K -topological spaces such as non- K -retractable spaces and some points deleted K -topological (finite) planes, and so on. To be specific, after proving that not every one point deleted subspace of a finite K -topological plane X is a K -retract of X , we study the FPP of a non-retractable topological space Y , such as one point deleted space Y ∖ { p } .

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:879-:d:269530
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    Citations

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    Cited by:

    1. 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.
    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 & Selma Özçağ, 2020. "The Fixed Point Property of the Infinite M -Sphere," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    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.

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