Extension problem of several continuities in computer topology
Bull. Korean Math. Soc. 2010 Vol. 47, No. 5, 915-932
https://doi.org/10.4134/BKMS.2010.47.5.915
Published online September 1, 2010
Sang-Eon Han
Chonbuk National University
Abstract : The goal of this paper is to study extension problems of several continuities in computer topology.To be specific, for a set $X \subset {\bf Z}^n$ take a subspace $(X, T_X^n)$ induced from the Khalimsky $n$D space $({\bf Z}^n, T^n)$. Considering $(X, T_X ^n)$ with one of the $k$-adjacency relations of ${\bf Z}^n$, 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.
Keywords : computer topology, digital topology, extension problem, Khalimsky topology, computer topological continuity, computer topological homeomorphism, $k$-retract
MSC numbers : 54C20, 54C05, 54D05, 54F05, 68U05
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