International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 471-476
doi:10.1155/S0161171201006482
Some applications of minimal open sets
Department of Applied Mathematics, Fukuoka University, Nanakuma Jonan-ku, Fukuoka 814-0180, Japan
Received 16 January 2001
Copyright © 2001 Fumie Nakaoka and Nobuyuki Oda. 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
We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a pre-Hausdorff space.