EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY

作者：Han Sang Eon^*

来源：Bulletin of the Korean Mathematical Society, 2010, 47(5): 915-932.

DOI：10.4134/BKMS.2010.47.5.915

• computer topology
• digital topology
• extension problem
• Khalimsky topology
• computer topological continuity
• computer topological homeomorphism
• k-retract

The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set X subset of Z(n) take a subspace (X, T(X)(n)) induced from the Khalimsky nD space (Z(n), T(n)). Considering (X, T(X)(n)) 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.

• 出版日期2010-9