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$𝒫$ -approximable compact spaces

Mihail G. Tkachenko (1991)

Commentationes Mathematicae Universitatis Carolinae

For every topological property $𝒫$ , we define the class of $𝒫$ -approximable spaces which consists of spaces X having a countable closed cover $γ$ such that the “section” $X (x, γ) = ⋂ {F \in γ : x \in F}$ has the property $𝒫$ for each $x \in X$ . It is shown that every $𝒫$ -approximable compact space has $𝒫$ , if $𝒫$ is one of the following properties: countable tightness, $ℵ_{0}$ -scatteredness with respect to character, $C$ -closedness, sequentiality (the last holds under MA or $2^{ℵ_{0}} < 2^{ℵ_{1}}$ ). Metrizable-approximable spaces are studied: every compact space in this class has...

...-Closed Mappings.

H.Z. Hdeib (1982)

Revista colombiana de matematicas

...-kompakte Räume.

Norbert Brunner (1982)

Manuscripta mathematica

$ℓ_{1}$ -partitions of unity on normed spaces

Zahradník, Miloš (1975)

Seminar Uniform Spaces

$α$ -paracompact subsets and well-situated subsets

Francisco Gallego Lupiañez (1988)

Czechoslovak Mathematical Journal

$ϰ$ -Lindelöf locales and their spatial parts

P. B. Johnson (1991)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

$τ$ -pseudocompact mappings.

Mironova, Yu.N. (2001)

Sibirskij Matematicheskij Zhurnal

$ω$ H-sets and cardinal invariants

Alessandro Fedeli (1998)

Commentationes Mathematicae Universitatis Carolinae

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 $A \subset ⋃ 𝒰$ there exists a countable subfamily $𝒱$ of $𝒰$ such that $A \subset ⋃ {\bar{V} : V \in 𝒱}$ . In this paper we introduce a new cardinal function $t_{s θ}$ and show that $| A | \leq 2^{t_{s θ} (X) ψ_{c} (X)}$ for every $ω$ H-set $A$ of a Hausdorff space $X$ .