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 + ¬ CH ] : ( * ) Let X be a Tychonoff space with c ( X ) ≤ 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.