Displaying similar documents to “The sizes of relatively compact T 1 -spaces”

The G δ -topology and incompactness of ω α

Isaac Gorelic (1996)

Commentationes Mathematicae Universitatis Carolinae

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We establish a relation between covering properties (e.gĿindelöf degree) of two standard topological spaces (Lemmas 4 and 5). Some cardinal inequalities follow as easy corollaries.

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 ) ≥ 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 ) ≥ κ .

Local cardinal functions of H-closed spaces

Angelo Bella, Jack R. Porter (1996)

Commentationes Mathematicae Universitatis Carolinae

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The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between H-closed and minimal Hausdorff spaces. An H-closed space X is produced with the properties that | X | > 2 2 ψ ( X ) and ψ ¯ ( X ) > 2 ψ ( X ) .

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel'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...