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EXTENSION PROBLEM OF SEVERAL CONTINUITIES IN COMPUTER TOPOLOGY

  • Han, Sang-Eon (FACULTY OF LIBERAL EDUCATION INSTITUTE OF PURE AND APPLIED MATHEMATICS CHONBUK NATIONAL UNIVERSITY)
  • Received : 2008.12.30
  • Published : 2010.09.30
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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.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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