On finite T₀ topological spaces

2002/04/10 by A. El-Fattah El-Atik, M. E. Abd El-Monsef, E. I. Lashin
Mathematics · #math.GN #msc:54B10 #msc:54D30 #msc:54A05 #msc:54G99

paper · pdf

published as Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 75--90, Topology Atlas, Toronto, 2002 · 16 pages

arxiv created 2002/04/10 · arxiv updated 2009/11/30

Abstract

Finite topological spaces became much more essential in topology, with the development of computer science. The task of this paper is to study and investigate some properties of such spaces with the existence of an ordered relation between their minimal neighborhoods. We introduce notations and elementary facts known as Alexandroff space. The family of minimal neighborhoods forms a unique minimal base. We consider T₀ spaces. We give a link between finite T₀ spaces and the related partial order. Finally, we study some properties of multifunctions and their relationships with connected ordered topological spaces.

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