Almost fixed point property for digital spaces associated with MarcusWyse topological spaces
Authors
SangEon Han
 Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, JeonjuCity Jeonbuk, 54896, Republic of Korea.
Abstract
The present paper studies almost fixed point property for digital spaces whose structures are induced by MarcusWyse
(M, for brevity) topology. In this paper we mainly deal with spaces \(X\) which are connected Mtopological spaces with Madjacency
(MAspaces or Mtopological graphs for short) whose cardinalities are greater than 1. Let MAC be a category whose objects,
denoted by Ob(MAC), are MAspaces and morphisms are MAmaps between MAspaces (for more details, see Section 3), and
MTC a category of Mtopological spaces as Ob(MTC) and Mcontinuous maps as morphisms of MTC (for more details, see
Section 3). We prove that whereas any MAspace does not have the fixed point property (FPP for short) for any MAmaps, a
bounded simple MApath has the almost fixed point property (AFPP for short). Finally, we refer the topological invariant of the
FPP for Mtopological spaces from the viewpoint of MTC.
Keywords
 Digital topology
 fixed point property
 MarcusWyse topology
 MAmap
 MAisomorphism
 MAhomotopy
 MAspace
 MAcontractibility
 Mtopological graph
 almost fixed point property.
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