SP-scattered spaces; a new generalization of scattered spaces

Melvin Henriksen; Robert M. Raphael; Grant R. Woods

Displaying similar documents to “SP-scattered spaces; a new generalization of scattered 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 $\leq 2$ 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...

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 $St (F, 𝒰) = ⋃ {U \in 𝒰 : U \cap F \neq \emptyset}$ . We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.

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...