International Journal of Mathematics and Mathematical Sciences (Jan 2007)

On P3-Paracompact Spaces

  • Khalid Al-Zoubi,
  • Samer Al-Ghour

DOI
https://doi.org/10.1155/2007/80697
Journal volume & issue
Vol. 2007

Abstract

Read online

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.