KD-(k0, k1)-HOMOTOPY EQUIVALENCE AND ITS APPLICATIONS

다국어 초록 (Multilingual Abstract)

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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