doi:10.1155/2007/80697 Research Article On P3-Paracompact Spaces

Mashhour et al. [1] introduced the notions of P1-paracompactness and P2-paracom pactness 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. Copyright © 2007 K. Al-Zoubi and S. Al-Ghour. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, dis-tribution, and reproduction in any medium, provided the original work is properly cited. 1