The Fixed Point Property of Non-Retractable Topological Spaces

Jeong Min Kang, Sang-Eon Han and Sik Lee
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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

Mathematics, 2019, vol. 7, issue 10, 1-12

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 } .

Keywords: Khalimsky topology; K -retraction; non- K -retractable space; fixed point property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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