Topological characterization of the small cardinal $i$

Antonio de Padua Franco-Filho

Nowhere dense subsets and Booth's Lemma

Viacheslav I. Malykhin (1996)

Commentationes Mathematicae Universitatis Carolinae

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The following statement is proved to be independent from $[LB + \neg CH]$ : $(*)$ Let $X$ be a Tychonoff space with $c (X) \leq ℵ_{0}$ and $π w (X) < ℭ$ . Then a union of less than $ℭ$ of nowhere dense subsets of $X$ is a union of not greater than $π w (X)$ of nowhere dense subsets.

Functional separability

Ronnie Levy, M. Matveev (2010)

Commentationes Mathematicae Universitatis Carolinae

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A space $X$ is functionally countable (FC) if for every continuous $f : X \to ℝ$ , $| f (X) | \leq ω$ . The class of FC spaces includes ordinals, some trees, compact scattered spaces, Lindelöf P-spaces, $σ$ -products in $2^{κ}$ , and some L-spaces. We consider the following three versions of functional separability: $X$ is 1-FS if it has a dense FC subspace; $X$ is 2-FS if there is a dense subspace $Y \subset X$ such that for every continuous $f : X \to ℝ$ , $| f (Y) | \leq ω$ ; $X$ is 3-FS if for every continuous $f : X \to ℝ$ , there is a dense subspace $Y \subset X$ such that $| f (Y) | \leq ω$ . We give examples...

Displaying similar documents to “Topological characterization of the small cardinal i ”

Nowhere dense subsets and Booth's Lemma

Functional separability

Displaying similar documents to “Topological characterization of the small cardinal $i$ ”