Open covers and function spaces.

Pansera, B.A.; Pavlović, V.

Displaying similar documents to “Open covers and function spaces.”

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.

Some weak covering properties and infinite games

Masami Sakai (2014)

Open Mathematics

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We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products...

On subsets of Alexandroff duplicates

Takemi Mizokami (2005)

Commentationes Mathematicae Universitatis Carolinae

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We characterize the subsets of the Alexandroff duplicate which have a G $_{δ}$ -diagonal and the subsets which are M-spaces in the sense of Morita.

On a problem of J. Nagata

Zi Qiu Yun (1989)

Commentationes Mathematicae Universitatis Carolinae

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