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ARRANGEMENT OF ELEMENTS OF LOCALLY FINITE TOPOLOGICAL SPACES UP TO AN ALF-HOMEOMORPHISM

Han, Sang-Eon;Chun, Woo-Jik

  • Received : 2011.10.11
  • Accepted : 2011.12.01
  • Published : 2011.12.25

Abstract

In relation to the classification of finite topological spaces the paper [17] studied various properties of finite topological spaces. Indeed, the study of future internet system can be very related to that of locally finite topological spaces with some order structures such as preorder, partial order, pretopology, Alexandroff topological structure and so forth. The paper generalizes the results from [17] so that the paper can enlarge topological and homotopic properties suggested in the category of finite topological spaces into those in the category of locally finite topological spaces including ALF spaces.

Keywords

Locally finite topological space;ALF space;homeomorphism;digital topology;Khalimsky topology;network

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Acknowledgement

Grant : Development of Future Internet common conceptual architecture and inter-operation techniques for trustworthy communication

Supported by : KCA