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On \(P_{3}\)-paracompact spaces. (English) Zbl 1139.54316

Summary: Mashhour, Abd El-Mouset and Hasanein introduced the notions of \(P_{1}\)-paracompactness and \(P_{2}\)-paracompactness of topological spaces in terms of preopen sets. In this paper, we introduce and investigate a weaker form of paracompactness which is called \(P_{3}\)-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 \(P_{3}\)-paracompact.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)

References:

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