International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 16, Article ID 18647, 8 pages
doi:10.1155/IJMMS/2006/18647
Minimal closed sets and maximal closed sets
Fumie Nakaoka
and Nobuyuki Oda
Department of Applied Mathematics, Fukuoka University, Nanakuma Jonan-ku, Fukuoka 814-0180, Japan
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.