International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 573038, 9 pages
doi:10.1155/2009/573038
Characterizations of strongly compact spaces
Ahmad Al-Omari1
, Takashi Noiri2
and Mohd.Salmi Md. Noorani3
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
Abstract
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 x∈A there exists a preopen set Ux containing x such that Ux−A is a finite set. We investigate some properties of the sets. Moreover, we obtain new characterizations and preserving theorems of strongly compact spaces.