Displaying similar documents to “Spaces with σ - n -linked topologies as special subspaces of separable spaces”

A compact ccc non-separable space from a Hausdorff gap and Martin's Axiom

Murray G. Bell (1996)

Commentationes Mathematicae Universitatis Carolinae

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We answer a question of I. Juhasz by showing that MA + ¬ CH does not imply that every compact ccc space of countable π -character is separable. The space constructed has the additional property that it does not map continuously onto I ω 1 .

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.

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 , | 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 , | f ( Y ) | ω ; X is 3-FS if for every continuous f : X , there is a dense subspace Y X such that | f ( Y ) | ω . We give examples...

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, 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...