EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY

EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY

The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set $X\;{\subset}\;Z^n$ take a subspace (X, $T_n^X$) induced from the Khalimsky nD space ($Z^n$, $T^n$). Considering (X, $T_n^X$) with one of the k-adjacency relations of $Z^n$, we call it a computer topological space (or a space if not confused) denoted by $X_{n,k}$. In addition, we introduce several kinds of k-retracts of $X_{n,k}$, 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.