Displaying similar documents to “On function spaces of Corson-compact spaces”

Continuous selections on spaces of continuous functions

Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

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For a space Z , we denote by ℱ ( Z ) , 𝒦 ( Z ) and ℱ 2 ( Z ) the hyperspaces of non-empty closed, compact, and subsets of cardinality ≤ 2 of Z , respectively, with their Vietoris topology. For spaces X and E , C p ( X , E ) is the space of continuous functions from X to E with its pointwise convergence topology. We analyze in this article when ℱ ( Z ) , 𝒦 ( Z ) and ℱ 2 ( Z ) have continuous selections for a space Z of the form C p ( X , E ) , where X is zero-dimensional and E is a strongly zero-dimensional metrizable space. We prove that C p ( X , E ) is weakly orderable...

Embedding into discretely absolutely star-Lindelöf spaces

Yan-Kui Song (2007)

Commentationes Mathematicae Universitatis Carolinae

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A space X is if for every open cover 𝒰 of X and every dense subset D of X , there exists a countable subset F of D such that F is discrete closed in X and St ( F , 𝒰 ) = X , where St ( F , 𝒰 ) = ⋃ { U ∈ 𝒰 : U ∩ F ≠ ∅ } . We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.

On remote points, non-normality and π -weight ω 1

Sergei Logunov (2001)

Commentationes Mathematicae Universitatis Carolinae

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We show, in particular, that every remote point of X is a nonnormality point of β X if X is a locally compact Lindelöf separable space without isolated points and π w ( X ) ≤ ω 1 .