International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 80697, 12 pages
doi:10.1155/2007/80697
On P3-Paracompact Spaces
Khalid Al-Zoubi1
and Samer Al-Ghour2
1Department of Mathematics, Faculty of Science, Yarmouk University, Irbid 21163, Jordan
2Department of Mathematics and Statistics, Faculty of Science, Jordan University of Science and Technology, Irbid 22110, Jordan
Abstract
Mashhour et al. [1] introduced the notions of P1-paracompactness and P2-paracompactness of topological spaces in terms of preopen sets. In this paper, we introduce and investigate a weaker form of paracompactness which is called P3-paracompact. We obtain various characterizations, properties, examples, and counterexamples concerning it and its relationships with other types of spaces. In particular, we show that if a space (X,T) is quasi-submaximal, then (X,T) is paracompact if it is P3-paracompact.