Two improvements on Tkačenko's addition theorem

János Gerlits; István Juhász; Zoltán Szentmiklóssy

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 $st - l (X) \geq κ$ .

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 “Two improvements on Tkačenko's addition theorem”

Spaces with large star cardinal number

Convergence in compacta and linear Lindelöfness