EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY

Title & Authors
EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY
Han, Sang-Eon;

Abstract
The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set $\small{X\;{\subset}\;Z^n}$ take a subspace (X, $\small{T_n^X}$) induced from the Khalimsky nD space ($\small{Z^n}$, $\small{T^n}$). Considering (X, $\small{T_n^X}$) with one of the k-adjacency relations of $\small{Z^n}$, we call it a computer topological space (or a space if not confused) denoted by $\small{X_{n,k}}$. In addition, we introduce several kinds of k-retracts of $\small{X_{n,k}}$, 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;
Language
English
Cited by
1.
ARRANGEMENT OF ELEMENTS OF LOCALLY FINITE TOPOLOGICAL SPACES UP TO AN ALF-HOMEOMORPHISM,;;

호남수학학술지, 2011. vol.33. 4, pp.617-628
2.
COMPARISON OF CONTINUITIES IN DIGITAL TOPOLOGY,;;

호남수학학술지, 2012. vol.34. 3, pp.451-465
1.
Extension of continuity of maps between axiomatic locally finite spaces, International Journal of Computer Mathematics, 2011, 88, 14, 2889
2.
ARRANGEMENT OF ELEMENTS OF LOCALLY FINITE TOPOLOGICAL SPACES UP TO AN ALF-HOMEOMORPHISM, Honam Mathematical Journal, 2011, 33, 4, 617
3.
COMPARISON OF CONTINUITIES IN DIGITAL TOPOLOGY, Honam Mathematical Journal, 2012, 34, 3, 451
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