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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 18647, 8 pages
http://dx.doi.org/10.1155/IJMMS/2006/18647

Minimal closed sets and maximal closed sets

Department of Applied Mathematics, Fukuoka University, Nanakuma Jonan-ku, Fukuoka 814-0180, Japan

Received 20 December 2005; Revised 28 May 2006; Accepted 6 August 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some properties of minimal closed sets and maximal closed sets are obtained, which are dual concepts of maximal open sets and minimal open sets, respectively. Common properties of minimal closed sets and minimal open sets are clarified; similarly, common properties of maximal closed sets and maximal open sets are obtained. Moreover, interrelations of these four concepts are studied.