On $\mathcal {L}$-starcompact spaces

Yan-Kui Song

Displaying similar documents to “On $ℒ$ -starcompact spaces”

Spaces with large relative extent

Yan-Kui Song (2007)

Czechoslovak Mathematical Journal

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In this paper, we prove the following statements: (1) For every regular uncountable cardinal $κ$ , there exist a Tychonoff space $X$ and $Y$ a subspace of $X$ such that $Y$ is both relatively absolute star-Lindelöf and relative property (a) in $X$ and $e (Y, X) \geq κ$ , but $Y$ is not strongly relative star-Lindelöf in $X$ and $X$ is not star-Lindelöf. (2) There exist a Tychonoff space $X$ and a subspace $Y$ of $X$ such that $Y$ is strongly relative star-Lindelöf in $X$ (hence, relative star-Lindelöf), but $Y$ is not absolutely relative...

Spaces with large star cardinal number

Yan-Kui Song (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we prove the following statements: (1) For any cardinal $κ$ , there exists a Tychonoff star-Lindelöf space $X$ such that $a (X) \geq κ$ . (2) There is a Tychonoff discretely star-Lindelöf space $X$ such that $a a (X)$ does not exist. (3) For any cardinal $κ$ , there exists a Tychonoff pseudocompact $σ$ -starcompact space $X$ such that $st - l (X) \geq κ$ .

Remarks on star covering properties in pseudocompact spaces

Yan-Kui Song (2013)

Mathematica Bohemica

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Let $P$ be a topological property. A space $X$ is said to be star $P$ if whenever $𝒰$ is an open cover of $X$ , there exists a subspace $A \subseteq X$ with property $P$ such that $X = St (A, 𝒰)$ , where $St (A, 𝒰) = ⋃ {U \in 𝒰 : U \cap A \neq \emptyset} .$ In this paper, we study the relationships of star $P$ properties for $P \in {Lindel ö f, compact, countablycompact}$ in pseudocompact spaces by giving some examples.

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel&#039;skii, Raushan Z. Buzyakova (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ be a compact Hausdorff space with a point $x$ such that $X ∖ {x}$ is linearly Lindelöf. Is then $X$ first countable at $x$ ? What if this is true for every $x$ in $X$ ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when $X$ is, in addition, $ω$ -monolithic. We also prove that if $X$ is compact, Hausdorff, and $X ∖ {x}$ is strongly discretely Lindelöf, for every $x$ in $X$ , then $X$ is first countable. An example of linearly...

Displaying similar documents to “On ℒ -starcompact spaces”

Spaces with large relative extent

Spaces with large star cardinal number

Remarks on star covering properties in pseudocompact spaces

Convergence in compacta and linear Lindelöfness

Displaying similar documents to “On $ℒ$ -starcompact spaces”