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Displaying similar documents to “Weak extent in normal spaces”

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 .