International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 471-476

Some applications of minimal open sets

Fumie Nakaoka and Nobuyuki Oda

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.


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.