Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces
Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces
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DOI：
10.22436/jnsa.010.01.04
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发表时间：
2017-01
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影响因子：
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通讯作者：
Sang-Eon Han
中科院分区：
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作者：
Sang-Eon Han
本文研究了由Marcus-Wyse （M-）拓扑结构诱导的数字空间的几乎不动点性质。本文主要研究基数大于1的m -邻接空间（ma -空间，简称m -拓扑图）的连通空间X。设MAC是一个范畴，其对象用Ob（MAC）表示为ma -空间，而态射是ma -空间之间的ma -映射（详细信息见第3节），MTC是一个m -拓扑空间的范畴，作为Ob（MTC）和m -连续映射，作为MTC的态射（详细信息见第3节）。我们证明了对于任意ma映射，任意ma空间不具有不动点性质（简称FPP），而有界简单ma路径具有几乎不动点性质（简称AFPP）。最后，从MTC的角度讨论了m -拓扑空间中FPP的拓扑不变量。C©2017版权所有。
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. c ©2017 all rights reserved.