EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY

Abstract. The goal of this paper is to study extension problems of sev-eral continuities in computer topology. To be specific, for a set X ⊂ Zn take a subspace (X,TnX) induced from the Khalimsky nD space (Z n, Tn). Considering (X,TnX) with one of the k-adjacency relations of Z n, we call it a computer topological space (or a space if not confused) denoted byXn,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. 1