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Displaying similar documents to “Densely continuous forms, pointwise topology and cardinal functions”

Metrization of function spaces with the Fell topology

Hanbiao Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

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For a Tychonoff space X , let ↓ C F ( X ) be the family of hypographs of all continuous maps from X to [ 0 , 1 ] endowed with the Fell topology. It is proved that X has a dense separable metrizable locally compact open subset if ↓ C F ( X ) is metrizable. Moreover, for a first-countable space X , ↓ C F ( X ) is metrizable if and only if X itself is a locally compact separable metrizable space. There exists a Tychonoff space X such that ↓ C F ( X ) is metrizable but X is not first-countable.

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...