On \(P_{3}\)-paracompact spaces (Q925461)
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scientific article; zbMATH DE number 5282533
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(P_{3}\)-paracompact spaces |
scientific article; zbMATH DE number 5282533 |
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On \(P_{3}\)-paracompact spaces (English)
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3 June 2008
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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.
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