Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces
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Authors
Sang-Eon Han
- Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, 54896, Jeonju-City Jeonbuk, Republic of Korea.
Abstract
The present paper studies almost fixed point property for digital spaces whose structures are induced by Marcus-Wyse
(M-, for brevity) topology. In this paper we mainly deal with spaces \(X\) which are connected M-topological spaces with M-adjacency
(MA-spaces or M-topological graphs for short) whose cardinalities are greater than 1. Let MAC be a category whose objects,
denoted by Ob(MAC), are MA-spaces and morphisms are MA-maps between MA-spaces (for more details, see Section 3), and
MTC a category of M-topological spaces as Ob(MTC) and M-continuous maps as morphisms of MTC (for more details, see
Section 3). We prove that whereas any MA-space does not have the fixed point property (FPP for short) for any MA-maps, a
bounded simple MA-path has the almost fixed point property (AFPP for short). Finally, we refer the topological invariant of the
FPP for M-topological spaces from the viewpoint of MTC.
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ISRP Style
Sang-Eon Han, Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 34--47
AMA Style
Han Sang-Eon, Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces. J. Nonlinear Sci. Appl. (2017); 10(1):34--47
Chicago/Turabian Style
Han, Sang-Eon. "Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 34--47
Keywords
- Digital topology
- fixed point property
- Marcus-Wyse topology
- MA-map
- MA-isomorphism
- MA-homotopy
- MA-space
- MA-contractibility
- M-topological graph
- almost fixed point property.
MSC
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