EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY
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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.
Abstract
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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