Displaying similar documents to “Spaces of continuous functions, box products and almost- ω -resolvable spaces”

Martin’s Axiom and ω -resolvability of Baire spaces

Fidel Casarrubias-Segura, Fernando Hernández-Hernández, Angel Tamariz-Mascarúa (2010)

Commentationes Mathematicae Universitatis Carolinae

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We prove that, assuming MA, every crowded T 0 space X is ω -resolvable if it satisfies one of the following properties: (1) it contains a π -network of cardinality < 𝔠 constituted by infinite sets, (2) χ ( X ) < 𝔠 , (3) X is a T 2 Baire space and c ( X ) ≤ ℵ 0 and (4) X is a T 1 Baire space and has a network 𝒩 with cardinality < 𝔠 and such that the collection of the finite elements in it constitutes a σ -locally finite family. Furthermore, we prove that the existence of a T 1 Baire irresolvable space is equivalent to the...

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...

On function spaces of Corson-compact spaces

Ingo Bandlow (1994)

Commentationes Mathematicae Universitatis Carolinae

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We apply elementary substructures to characterize the space C p ( X ) for Corson-compact spaces. As a result, we prove that a compact space X is Corson-compact, if C p ( X ) can be represented as a continuous image of a closed subspace of ( L τ ) ω × Z , where Z is compact and L τ denotes the canonical Lindelöf space of cardinality τ with one non-isolated point. This answers a question of Archangelskij [2].