DIGITAL TOPOLOGICAL PROPERTY OF THE DIGITAL 8-PSEUDOTORI

  • LEE, SIK (Department fo Applied Mathematics College of Natural Science, Yosu National University) ;
  • KIM, SAM-TAE (Department of Computer and Appiled Mathematics College of Natural Science, Honam University) ;
  • HAN, SANG-EON (Department of Computer and Applied Mathematics College of Natural Science, Honam University)
  • Received : 2004.09.07
  • Published : 2004.12.25

Abstract

A digital $(k_0,\;k_1)$-homotopy is induced from digital $(k_0,\;k_1)$-continuity with the n kinds of $k_i$-adjacency relations in ${\mathbb{Z}}^n$, $i{\in}\{0,\;1\}$. The k-fundamental group, ${\pi}^k_1(X,\;x_0)$, is derived from the pointed digital k-homotopy, $k{\in}\{3^n-1(n{\geq}2),\;3^n-{\sum}^{r-2}_{k=0}C^n_k2^{n-k}-1(2{\leq}r{\leq}n-1(n{\geq}3)),\;2n(n{\geq}1)\}$. In this paper two kinds of digital 8-pseudotori stemmed from the minimal simple closed 4-curve and the minimal simple closed 8-curve with 8-contractibility or without 8-contractibility, e.g., $DT_8$ and $DT^{\prime}_8$, are introduced and their digital topological properties are studied by the calculation of the k-fundamental groups, $k{\in}\{8,\;32,\;64,\;80\}$.

Keywords

digital k-neighborhood;k-contractibility;digital $(k_0,\;k_1)$-homotopy;k-fundamental group;digital $(k_0,\;k_1)$-homeomorphism;digital covering space;product space;digital 8-pseudotorus

Acknowledgement

Supported by : Yosu National University

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