On the extent of star countable spaces

Ofelia Alas; Lucia Junqueira; Jan Mill; Vladimir Tkachuk; Richard Wilson

Displaying similar documents to “On the extent of star countable spaces”

Remarks on absolutely star countable spaces

Yan-Kui Song (2013)

Open Mathematics

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We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed...

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.

First countable and countable spaces all compactifications of which contain βN

Eric van Douwen, Teodor Przymusiński (1979)

Fundamenta Mathematicae

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On weaker forms of compactness, Lindelöfness, and countable compactness.

Baboolal, D., Backhouse, J., Ori, R.G. (1990)

International Journal of Mathematics and Mathematical Sciences

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A note on the extent of two subclasses of star countable spaces

Zuoming Yu (2012)

Open Mathematics

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We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.

Countable And Uncountable Covers

H. P. Tan (1973)

Publications de l'Institut Mathématique

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First countable spaces without point-countable π-bases

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2007)

Fundamenta Mathematicae

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We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that ∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large); ∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ; ∙ it is consistent to have a...

A lattice of conditions on topological spaces II

P. Moody, G. Reed, A. Roscoe, P. Collins (1991)

Fundamenta Mathematicae

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Countable fan-tightness versus countable tightness

Aleksander V. Arhangel&#039;skii, Angelo Bella (1996)

Commentationes Mathematicae Universitatis Carolinae

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Countable tightness is compared to the stronger notion of countable fan-tightness. In particular, we prove that countable tightness is equivalent to countable fan-tightness in countably compact regular spaces, and that countable fan-tightness is preserved by pseudo-open compact mappings. We also discuss the behaviour of countable tightness and of countable fan-tightness under the product operation.