Displaying similar documents to “Metrization of function spaces with the Fell topology”

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

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In this note we first give a summary that on property of a remainder of a non-locally compact topological group G in a compactification b G makes the remainder and the topological group G all separable and metrizable. If a non-locally compact topological group G has a compactification b G such that the remainder b G ∖ G of G belongs to 𝒫 , then G and b G ∖ G are separable and metrizable, where 𝒫 is a class of spaces which satisfies the following conditions: (1) if X ∈ 𝒫 , then every compact subset of the...

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...

Functional separability

Ronnie Levy, M. Matveev (2010)

Commentationes Mathematicae Universitatis Carolinae

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A space X is functionally countable (FC) if for every continuous f : X → ℝ , | f ( X ) | ≤ ω . The class of FC spaces includes ordinals, some trees, compact scattered spaces, Lindelöf P-spaces, σ -products in 2 κ , and some L-spaces. We consider the following three versions of functional separability: X is 1-FS if it has a dense FC subspace; X is 2-FS if there is a dense subspace Y ⊂ X such that for every continuous f : X → ℝ , | f ( Y ) | ≤ ω ; X is 3-FS if for every continuous f : X → ℝ , there is a dense subspace Y ⊂ X such that | f ( Y ) | ≤ ω . We give examples...