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Displaying similar documents to “On nearly discrete spaces”

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 2 ℵ 0 = 2 ℵ 1 , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.