Some weak covering properties and infinite games

Masami Sakai

Displaying similar documents to “Some weak covering properties and infinite games”

A note on the extent of two subclasses of star countable spaces

Zuoming Yu (2012)

Open Mathematics

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We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.

Monotone weak Lindelöfness

Maddalena Bonanzinga, Filippo Cammaroto, Bruno Pansera (2011)

Open Mathematics

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The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and...

K-space function spaces.

McCoy, R.A. (1980)

International Journal of Mathematics and Mathematical Sciences

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Remarks on absolutely star countable spaces

Yan-Kui Song (2013)

Open Mathematics

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We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed...

Weakly infinite-dimensional compactifications and countable-dimensional compactifications

Takashi Kimura, Chieko Komoda (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we give a characterization of a separable metrizable space having a metrizable S-weakly infinite-dimensional compactification in terms of a special metric. Moreover, we give two characterizations of a separable metrizable space having a metrizable countable-dimensional compactification.

A semifilter approach to selection principles

Lubomyr Zdomsky (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal $𝔤$ is a lower bound of the additivity number of the $σ$ -ideal generated by Menger subspaces of the Baire space, and under $𝔲 < 𝔤$ every subset $X$ of the real line with the property $Split (Λ, Λ)$ is Hurewicz, and thus it is consistent with ZFC that the property $Split (Λ, Λ)$ is preserved by unions of less than $𝔟$ subsets of the real line.