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Let Zn be the Cartesian product of the set of integers Z and let (Z, T) and (Zn, Tn) be the Khalimsky line topology on Z and the Khalimsky product topology on Zn, respectively. Then for a set X⊂ Zn,consider the subspace (X, TnX ) induced from (Zn, Tn). Considering a k-adjacency on (X, TnX ), we call it a (computer topological) space with k-adjacency and use the notation (X, k, TnX ) := Xn,k. In this paper we introduce the notions of KD-(k0, k1)-homotopy equivalence and KD-kdeformation retract and investigate a classification of (computer topological)spaces Xn,k in terms of a KD-(k0, k1)-homotopy equivalence.
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참고문헌 (32)
참고문헌 신청
E. Khalimsky / 1991 / Computer graphics and connected topologies on finite ordered sets / Topology and its Applications 36 (1) : 1 ~ 17
G. Gierz / 1980 / A Compendium of Continuous Lattices / Springer-Verlag
I.-S. Kim / 2010 / The almost pasting property of digital continuity / Acta Applicandae Mathematicae 110 (1) : 399 ~ 408
J. Dontchev / 1999 / Groups of μ-generalized homeomorphisms and the digital line / Topology Appl. 95 (2) : 113 ~ 128
L. Boxer / 1994 / Digitally continuous functions / Pattern Recognition Letters 15 : 833 ~ 839
G. Gierz / 1980 / A Compendium of Continuous Lattices / Springer-Verlag
I.-S. Kim / 2010 / The almost pasting property of digital continuity / Acta Applicandae Mathematicae 110 (1) : 399 ~ 408
J. Dontchev / 1999 / Groups of μ-generalized homeomorphisms and the digital line / Topology Appl. 95 (2) : 113 ~ 128
L. Boxer / 1994 / Digitally continuous functions / Pattern Recognition Letters 15 : 833 ~ 839
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