Spaces of continuous functions, box products and almost-$\omega $-resolvable spaces

Angel Tamariz-Mascarúa; H. Villegas-Rodríguez

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 $c (X) \leq ℵ_{0}$ 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 $\leq 2$ 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 ${(L_{τ})}^{ω} \times Z$ , 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].

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

Martin’s Axiom and ω -resolvability of Baire spaces

Continuous selections on spaces of continuous functions

On function spaces of Corson-compact spaces

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

Martin’s Axiom and $ω$ -resolvability of Baire spaces