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Displaying similar documents to “Natural sinks on Y β

Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness

Vassiliki Farmaki (2002)

Fundamenta Mathematicae

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We study the c₀-content of a seminormalized basic sequence (χₙ) in a Banach space, by the use of ordinal indices (taking values up to ω₁) that determine dichotomies at every ordinal stage, based on the Ramsey-type principle for every countable ordinal, obtained earlier by the author. We introduce two such indices, the c₀-index ξ ( χ ) and the semibounded completeness index ξ b ( χ ) , and we examine their relationship. The countable ordinal values that these indices can take are always of the form...

Interpolation of κ -compactness and PCF

István Juhász, Zoltán Szentmiklóssy (2009)

Commentationes Mathematicae Universitatis Carolinae

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We call a topological space κ -compact if every subset of size κ has a complete accumulation point in it. Let Φ ( μ , κ , λ ) denote the following statement: μ < κ < λ = cf ( λ ) and there is { S ξ : ξ < λ } [ κ ] μ such that | { ξ : | S ξ A | = μ } | < λ whenever A [ κ ] < κ . We show that if Φ ( μ , κ , λ ) holds and the space X is both μ -compact and λ -compact then X is κ -compact as well. Moreover, from PCF theory we deduce Φ ( cf ( κ ) , κ , κ + ) for every singular cardinal κ . As a corollary we get that a linearly Lindelöf and ω -compact space is uncountably compact, that is κ -compact for all uncountable cardinals...

ω H-sets and cardinal invariants

Alessandro Fedeli (1998)

Commentationes Mathematicae Universitatis Carolinae

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A subset A of a Hausdorff space X is called an ω H-set in X if for every open family 𝒰 in X such that A 𝒰 there exists a countable subfamily 𝒱 of 𝒰 such that A { V ¯ : V 𝒱 } . In this paper we introduce a new cardinal function t s θ and show that | A | 2 t s θ ( X ) ψ c ( X ) for every ω H-set A of a Hausdorff space X .