International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 80697, 12 pages
Research Article

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

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.


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.