Spaces with large star cardinal number

Yan-Kui Song

Displaying similar documents to “Spaces with large star cardinal number”

On $ℒ$ -starcompact spaces

Yan-Kui Song (2006)

Czechoslovak Mathematical Journal

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A space $X$ is $ℒ$ -starcompact if for every open cover $𝒰$ of $X,$ there exists a Lindelöf subset $L$ of $X$ such that $S t (L, 𝒰) = X .$ We clarify the relations between $ℒ$ -starcompact spaces and other related spaces and investigate topological properties of $ℒ$ -starcompact spaces. A question of Hiremath is answered.

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...

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...

Displaying similar documents to “Spaces with large star cardinal number”

On ℒ -starcompact spaces

Convergence in compacta and linear Lindelöfness

Spaces with large relative extent

On $ℒ$ -starcompact spaces