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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 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, 0 -scatteredness with respect to character, C -closedness, sequentiality (the last holds under MA or 2 0 < 2 1 ). Metrizable-approximable spaces are studied: every compact space in this class has...

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