On <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mtext>P</mml:mtext><mml:mn>3</mml:mn></mml:msub></mml:math>-Paracompact Spaces

Al-Zoubi, Khalid; Al-Ghour, Samer

doi:https://doi.org/10.1155/2007/80697

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 080697 | https://doi.org/10.1155/2007/80697

On P3-Paracompact Spaces

Khalid Al-Zoubi¹and Samer Al-Ghour²

Academic Editor: Etienne E. Kerre

Received09 Apr 2007

Accepted06 Aug 2007

Published04 Nov 2007

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.

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Copyright

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.

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