Displaying similar documents to “Order-like structure of monotonically normal spaces”

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...

On 𝒞 -starcompact spaces

Yan-Kui Song (2008)

Mathematica Bohemica

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A space X is if for every open cover 𝒰 of X , there exists a countably compact subset C of X such that St ( C , 𝒰 ) = X . In this paper we investigate the relations between 𝒞 -starcompact spaces and other related spaces, and also study topological properties of 𝒞 -starcompact spaces.

Cardinal invariants and compactifications

Anatoly A. Gryzlov (1994)

Commentationes Mathematicae Universitatis Carolinae

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We prove that every compact space X is a Čech-Stone compactification of a normal subspace of cardinality at most d ( X ) t ( X ) , and some facts about cardinal invariants of compact spaces.