Results 11 to 20 of about 75 (63)
The semi-T3-separation axiom of Khalimsky topological spaces
Filomat, 2023 The paper initially studies both the s-T3-separation and the semi-T3-separation axiom of Khalimsky (K-for brevity) topological spaces. To do this work, first we investigate some properties of semi-open and semi-closed sets with respect to the operations of union or intersection and further, a homeomorphism, and a semi-homeomorphism.
Sang-Eon Han, Selma Özçağ
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Contractibility of the digital $n$-space
Applied General Topology, 2015 The aim of this paper is to prove a known fact that the digital line is cotractible. Hence we have that the digital space $({\bf Z}^{n}, \kappa^{n})$ is also cotractible where $({\bf Z}^{n}, \kappa^{n})$ is $n$ products of the digital line $({\bf Z ...
Sayaka Hamada
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Continuous extension in topological digital spaces
Applied General Topology, 2008 We give necessary and sufficient conditions for the existence of a continuous extension from a smallest-neighborhood space (Alexandrov space) X to the Khalimsky line. Using this result, we classify the subsets A X such that every continuous function A !
Erik Melin
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Compression of Khalimsky topological spaces
Filomat, 2012 Aiming at the study of the compression of Khalimsky topological spaces which is an interesting field in digital geometry and computer science, the present paper develops a new homotopy thinning suitable for the work. Since Khalimsky continuity of maps between Khalimsky topological spaces has some limitations of performing a discrete ...
Min Kang, Sang-Eon Han
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Mathematics, 2019 This paper explores a certain relationship between the almost fixed point property (AFPP for short) of a compact and n-dimensional Euclidean space and that of its digitized space.
Sang-Eon Han
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A ternary relation for structuring the digital plane
ITM Web of Conferences, 2017 We discuss certain ternary relations, called plain, and show that each of them induces a connectedness on its underlying set. This connectedness allows for definitions of concepts of simple closed and Jordan curves.
Šlapal Josef
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Concerning Cut Point Spaces of Order Three
International Journal of Mathematics and Mathematical Sciences, Volume 2007, Issue 1, 2007., 2007 A point p of a topological space X is a cut point of X if X − {p} is disconnected. Further, if X − {p} has precisely m components for some natural number m ≥ 2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space.
D. Daniel +2 more
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The Khalimsky Line Topology- Countability and Connectedness
International Journal of Chemistry, Mathematics and Physics, 2022 The concepts of connectedness and countability in digital image processing are used for establishing boundaries of objects and components of regions in an image. The purpose of this paper is to investigate some notions of connectedness and countability of Khalimsky line topology.
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The compactificability classes of certain spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We apply the theory of the mutual compactificability to some spaces, mostly derived from the real line. For example, any noncompact locally connected metrizable generalized continuum, the Tichonov cube without its zero point Iℵ0\{0}, as well as the Cantor discontinuum without its zero point Dℵ0\{0} are of the same class of mutual compactificability as ...
Martin Maria Kovár
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The Fixed Point Property of Non-Retractable Topological Spaces
Mathematics, 2019 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.
Jeong Min Kang, Sang-Eon Han, Sik Lee
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