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The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set X ⊂Zn take a subspace (X, TnX ) induced from the Khalimsky nD space (Zn, Tn).
Considering (X, TnX ) with one of the k-adjacency relations of Zn, we call it a computer topological space (or a space if not confused) denoted by Xn,k.
In addition, we introduce several kinds of k-retracts of Xn,k, investigate their properties related to several continuities and homeomorphisms in computer topology and study extension problems of these continuities in relation with these k-retracts.
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참고문헌 (20)
참고문헌 신청
A. Rosenfeld / 1973 / Arcs and curves in digital pictures / J. Assoc. Comput. Mach. 20 : 81 ~ 87
E. Khalimsky / 1990 / Computer graphics and connected topologies on finite ordered sets / Topology Appl. 36 (1) : 1 ~ 17
E. Melin / 2005 / Extension of continuous functions in digital spaces with the Khalimsky topology / Topology Appl. 153 (1) : 52 ~ 65
G. Gierz / 1980 / A Compendium of Continuous Lattices / Springer
I.-S. Kim / 2010 / The pasting property of digital continuity / Acta Appl. Math. 110 (1) : 399 ~ 408
E. Khalimsky / 1990 / Computer graphics and connected topologies on finite ordered sets / Topology Appl. 36 (1) : 1 ~ 17
E. Melin / 2005 / Extension of continuous functions in digital spaces with the Khalimsky topology / Topology Appl. 153 (1) : 52 ~ 65
G. Gierz / 1980 / A Compendium of Continuous Lattices / Springer
I.-S. Kim / 2010 / The pasting property of digital continuity / Acta Appl. Math. 110 (1) : 399 ~ 408
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