Cardinal inequalities implying maximal resolvability

Marek Balcerzak; Tomasz Natkaniec; Małgorzata Terepeta

Displaying similar documents to “Cardinal inequalities implying maximal resolvability”

Nowhere dense subsets and Booth's Lemma

Viacheslav I. Malykhin (1996)

Commentationes Mathematicae Universitatis Carolinae

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The following statement is proved to be independent from $[LB + \neg CH]$ : $(*)$ Let $X$ be a Tychonoff space with $c (X) \leq ℵ_{0}$ and $π w (X) < ℭ$ . Then a union of less than $ℭ$ of nowhere dense subsets of $X$ is a union of not greater than $π w (X)$ of nowhere dense subsets.

On $π$ -caliber and an application of Prikry’s partial order

Andrzej Szymański (2011)

Commentationes Mathematicae Universitatis Carolinae

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We study the concept of $π$ -caliber as an alternative to the well known concept of caliber. $π$ -caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, $π$ -caliber may take on values below the Souslin number of a space. Under Martin’s axiom, $2^{ω}$ is a $π$ -caliber of $ℕ^{*}$ . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.

On $𝒞$ -starcompact spaces

Yan-Kui Song (2008)

Mathematica Bohemica

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A space $X$ is if for every open cover $𝒰$ of $X,$ there exists a countably compact subset $C$ of $X$ such that $St (C, 𝒰) = X .$ In this paper we investigate the relations between $𝒞$ -starcompact spaces and other related spaces, and also study topological properties of $𝒞$ -starcompact spaces.

Displaying similar documents to “Cardinal inequalities implying maximal resolvability”

Nowhere dense subsets and Booth's Lemma

On π -caliber and an application of Prikry’s partial order

On 𝒞 -starcompact spaces

On $π$ -caliber and an application of Prikry’s partial order

On $𝒞$ -starcompact spaces