A generalization of Čech-complete spaces and Lindelöf $\Sigma $-spaces

Aleksander V. Arhangel'skii

H-closed extensions with countable remainder

Daniel K. McNeill (2012)

Commentationes Mathematicae Universitatis Carolinae

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This paper investigates necessary and sufficient conditions for a space to have an H-closed extension with countable remainder. For countable spaces we are able to give two characterizations of those spaces admitting an H-closed extension with countable remainder. The general case is more difficult, however, we arrive at a necessary condition — a generalization of Čech completeness, and several sufficient conditions for a space to have an H-closed extension with countable remainder....

$𝒫$ -approximable compact spaces

Mihail G. Tkachenko (1991)

Commentationes Mathematicae Universitatis Carolinae

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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...

Displaying similar documents to “A generalization of Čech-complete spaces and Lindelöf Σ -spaces”

H-closed extensions with countable remainder

𝒫 -approximable compact spaces

Displaying similar documents to “A generalization of Čech-complete spaces and Lindelöf $Σ$ -spaces”

$𝒫$ -approximable compact spaces