Bull. Korean Math. Soc. 2010; 47(5): 915-932
Printed September 1, 2010
https://doi.org/10.4134/BKMS.2010.47.5.915
Copyright © The Korean Mathematical Society.
Sang-Eon Han
Chonbuk National University
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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