Classification of Spaces in Terms of Both a Digitization and a Marcus Wyse Topological Structure

Han, Sang-Eon; Chun, Woo-Jik

doi:10.5831/hmj.2011.33.4.575

Cited by 12 publications

(14 citation statements)

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“…Let us now recall the M-topological category and an M-homeomorphism [16] as follows: Owing to the Alexandroff topological structure of M-topology, M-continuity of a map between M-topological spaces is defined as follows:…”

Section: Some Properties Of Categories Associated With the M-topologimentioning

confidence: 99%

“…Digital topology focuses on studying digital topological properties of nD digital spaces [7,26,27], which has contributed to some areas of computer sciences such as computer graphics, image processing, mathematical morphology and so forth. In digital topology, although there are several approaches of studying digital images [1,7,11,15,16,20,22,26,29], the present paper follows an M-topological approach [13,19,29]. Since M-topology is considered in the Euclidean 2D space with integer coordinates, it plays an important role in digital topology and digital geometry.…”

Section: Introductionmentioning

confidence: 99%

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Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces

Han¹

2017

J. Nonlinear Sci. Appl.

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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(MT C) 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 MT C. c 2017 all rights reserved.

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Section: Some Properties Of Categories Associated With the M-topologimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces

Han¹

2017

J. Nonlinear Sci. Appl.

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“…The recent paper [12] established the notion of an LM A-map associated with both M -topology and an M -localized neighborhood in [10].…”

Section: Generalization Of An Lm A-mapmentioning

confidence: 99%

“…Using M -continuous maps, we obtain the M -topological category, denoted by MTC [10,8], consisting of the following two sets:…”

Section: Generalization Of An Lm A-mapmentioning

confidence: 99%

“…To study the digitization of subspaces (X, E 2 X ) of (R 2 , E 2 ) in the Mtopological approach, the papers [10,12,14] proposed an M A-digitization and studies it properties, which can be used to study some properties Meanwhile, to study the digitization of subspaces (X, E n X ) of (R n , E n ) in a K-topological approach, the paper [7,14] proposed a KA-digitization and further, the paper [7] proposed the notion of lattice-based K-adjacency (LA-, for short) map, which also contributed to a KA-digitization of subspaces of R n .…”

Section: Introductionmentioning

confidence: 99%

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