International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 573038, 9 pages
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 is said to be strongly compact if every preopen cover of 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
is said to be 𝒩-preopen if for each
there exists a preopen set
containing such that is a finite
set. We investigate some properties of the sets. Moreover, we obtain new characterizations and preserving theorems of strongly compact spaces.