International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 80697, 12 pages
doi:10.1155/2007/80697
Research Article
On P3-Paracompact Spaces
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
Received 9 April 2007; Accepted 6 August 2007
Academic Editor: Etienne E. Kerre
Copyright © 2007 Khalid Al-Zoubi and Samer Al-Ghour. 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.
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.