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

Let Z n be the Cartesian product of the set of integers Z and let (Z,T) and (Z n ,T n ) be the Khalimsky line topology on Z and the Khalimsky product topology onZ n , respectively. Then for a set X ‰Z n , consider the subspace (X,T n X) induced from (Z n ,T n ). Considering a k-adjacency on (X,T n X), we call it a (computer topological) space with k-adjacency and use the notation (X,k,Tn X ) := Xn,k. In this paper we