VARIOUS CONTINUITIES OF A MAP f ; (X, k, TnX) → (Y, 2, TY) IN COMPUTER TOPOLOGY

  • HAN, SANG-EON (Department of Computer and Applied Mathematics Honam University)
  • Received : 2006.10.11
  • Published : 2006.12.31

Abstract

For a set $X{\subset}{\mathbb{Z}}^n$ let $(X,\;T^n_X)$ be the subspace of the Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$, $n{\in}N$. Considering a k-adjacency of $(X,\;T^n_X)$, we use the notation $(X,\;k,\;T^n_X)$. In this paper for a map $$f:(X,\;k,\;T^n_X){\rightarrow}(Y,\;2\;T_Y)$$, we find the condition that weak (k, 2)-continuity of the map f implies strong (k, 2)-continuity of f.

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