$LJ$-spaces

Yin-Zhu Gao

Displaying similar documents to “ $L J$ -spaces”

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.

An independency result in connectification theory

Alessandro Fedeli, Attilio Le Donne (1999)

Commentationes Mathematicae Universitatis Carolinae

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A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let $ψ$ be the following statement: “a perfect $T_{3}$ -space $X$ with no more than $2^{𝔠}$ clopen subsets is connectifiable if and only if no proper nonempty clopen subset of $X$ is feebly compact". In this note we show that neither $ψ$ nor $\neg ψ$ is provable in ZFC.

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 “ L J -spaces”

On ℒ -starcompact spaces

An independency result in connectification theory

Spaces with large relative extent

Displaying similar documents to “ $L J$ -spaces”

On $ℒ$ -starcompact spaces