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The Fixed Point Property of Non-Retractable Topological Spaces.
- Source :
- Mathematics (2227-7390); Oct2019, Vol. 7 Issue 10, p879-879, 1p
- Publication Year :
- 2019
-
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 } . [ABSTRACT FROM AUTHOR]
- Subjects :
- TOPOLOGICAL spaces
FIXED point theory
TOPOLOGICAL property
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Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 7
- Issue :
- 10
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 139693065
- Full Text :
- https://doi.org/10.3390/math7100879