Topology Atlas
Document # ppae-08

## On finite T_{0} topological spaces

### A. El-Fattah El-Atik, M. E. Abd El-Monsef and E. I. Lashin

Proceedings of the Ninth Prague Topological Symposium
(2001)
pp. 75-90
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 T_{0} spaces.
We give a link between finite T_{0} spaces and the related partial order.
Finally, we study some properties of multifunctions and their
relationships with connected ordered topological spaces.

Mathematics Subject Classification. 54B10 54D30 (54A05 54G99).

Keywords. $T_0$ spaces, finite $T_0$ spaces, minimal neighborhoods,
partially ordered sets, multifunctions, topological dimension, weak
continuity.

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Copyright © 2002
Charles University and
Topology Atlas.
Published April 2002.