Embedding into discretely absolutely star-Lindelöf spaces

Yan-Kui Song

Displaying similar documents to “Embedding into discretely absolutely star-Lindelöf spaces”

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].

Condensations of Cartesian products

Oleg I. Pavlov (1999)

Commentationes Mathematicae Universitatis Carolinae

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We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space $X$ there is a $μ$ such that $X^{μ}$ can be condensed onto a normal ( $σ$ -compact) space if and only if there is no measurable cardinal. For any Tychonoff space $X$ and any cardinal $ν$ there is a Tychonoff space $M$ which preserves many properties of $X$ and such that any one-to-one continuous image of $M^{μ}$ , $μ \leq ν$ , contains a...

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...