Displaying similar documents to “Interpolation of κ -compactness and PCF”

Initially κ -compact spaces for large κ

Stavros Christodoulou (1999)

Commentationes Mathematicae Universitatis Carolinae

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This work presents some cardinal inequalities in which appears the closed pseudo-character, ψ c , of a space. Using one of them — ψ c ( X ) 2 d ( X ) for T 2 spaces — we improve, from T 3 to T 2 spaces, the well-known result that initially κ -compact T 3 spaces are λ -bounded for all cardinals λ such that 2 λ κ . And then, using an idea of A. Dow, we prove that initially κ -compact T 2 spaces are in fact compact for κ = 2 F ( X ) , 2 s ( X ) , 2 t ( X ) , 2 χ ( X ) , 2 ψ c ( X ) or κ = max { τ + , τ < τ } , where τ > t ( p , X ) for all p X .

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 .

A solution to Comfort's question on the countable compactness of powers of a topological group

Artur Hideyuki Tomita (2005)

Fundamenta Mathematicae

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In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number α 2 , a topological group G such that G γ is countably compact for all cardinals γ < α, but G α is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under M A c o u n t a b l e . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from M A c o u n t a b l e . However, the question has...