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EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY

Han, Sang-Eon

  • Received : 2008.12.30
  • Published : 2010.09.30

Abstract

The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set $X\;{\subset}\;Z^n$ 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.

Keywords

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

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Cited by

  1. Extension of continuity of maps between axiomatic locally finite spaces vol.88, pp.14, 2011, https://doi.org/10.1080/00207160.2011.577892
  2. ARRANGEMENT OF ELEMENTS OF LOCALLY FINITE TOPOLOGICAL SPACES UP TO AN ALF-HOMEOMORPHISM vol.33, pp.4, 2011, https://doi.org/10.5831/HMJ.2011.33.4.617
  3. COMPARISON OF CONTINUITIES IN DIGITAL TOPOLOGY vol.34, pp.3, 2012, https://doi.org/10.5831/HMJ.2012.34.3.451

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)