International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 573038, 9 pages
Research Article

Characterizations of Strongly Compact Spaces

1Department of Mathematics and Statistics, Faculty of Science, Mu'tah University, P.O. Box 7, Karak 61710, Jordan
22949-1 Shiokita-cho, Hinagu, Yatsushiro-shi, Kumamoto-ken 869-5142, Japan
3School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 4 July 2009; Accepted 30 September 2009

Academic Editor: Richard Wilson

Copyright © 2009 Ahmad Al-Omari et al. 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.


A topological space (X,τ) is said to be strongly compact if every preopen cover of (X,τ) admits a finite subcover. In this paper, we introduce a new class of sets called 𝒩-preopen sets which is weaker than both open sets and 𝒩-open sets. Where a subset A is said to be 𝒩-preopen if for each xA there exists a preopen set Ux containing x such that UxA is a finite set. We investigate some properties of the sets. Moreover, we obtain new characterizations and preserving theorems of strongly compact spaces.