Discrete subsets in Hausdorff topoligies.
Horacio Porta, Lázaro Recht (1987)
Collectanea Mathematica
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Displaying similar documents to “On nearly discrete spaces”
Discrete subsets in Hausdorff topoligies.
Small subsets of first countable spaces
Eric van Douwen, Michael Wage (1979)
Fundamenta Mathematicae
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A note on discrete sets
Santi Spadaro (2009)
Commentationes Mathematicae Universitatis Carolinae
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We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.
Remarks on star countable discrete closed spaces
Yan-Kui Song (2013)
Czechoslovak Mathematical Journal
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In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.
Some properties of the discrete holometric space
Vijayakumar, A. (1985-1986)
Portugaliae mathematica
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Closed discrete subsets of separable spaces and relative versions of normality, countable paracompactness and property
Samuel Gomes da Silva (2011)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we show that a separable space cannot include closed discrete subsets which have the cardinality of the continuum and satisfy relative versions of any of the following topological properties: normality, countable paracompactness and property . It follows that it is consistent that closed discrete subsets of a separable space which are also relatively normal (relatively countably paracompact, relatively ) in are necessarily countable. There are, however, consistent...