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Displaying similar documents to “Rigid extensions of ℓ -groups of continuous functions”

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 ∈ γ : x ∈ F } has the property 𝒫 for each x ∈ 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...

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....

Nowhere dense subsets and Booth's Lemma

Viacheslav I. Malykhin (1996)

Commentationes Mathematicae Universitatis Carolinae

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The following statement is proved to be independent from [ LB + ¬ CH ] : ( * ) Let X be a Tychonoff space with c ( X ) ≤ ℵ 0 and π w ( X ) < ℭ . Then a union of less than ℭ of nowhere dense subsets of X is a union of not greater than π w ( X ) of nowhere dense subsets.