On embeddings into $C_p(X)$ where $X$ is Lindelöf

Masami Sakai

Displaying similar documents to “On embeddings into $C_{p} (X)$ where $X$ is Lindelöf”

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...

A remark on the tightness of products

Oleg Okunev (1996)

Commentationes Mathematicae Universitatis Carolinae

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We observe the existence of a $σ$ -compact, separable topological group $G$ and a countable topological group $H$ such that the tightness of $G$ is countable, but the tightness of $G \times H$ is equal to $𝔠$ .

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel&#039;skii, Raushan Z. Buzyakova (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ be a compact Hausdorff space with a point $x$ such that $X ∖ {x}$ is linearly Lindelöf. Is then $X$ first countable at $x$ ? What if this is true for every $x$ in $X$ ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when $X$ is, in addition, $ω$ -monolithic. We also prove that if $X$ is compact, Hausdorff, and $X ∖ {x}$ is strongly discretely Lindelöf, for every $x$ in $X$ , then $X$ is first countable. An example of linearly...

Displaying similar documents to “On embeddings into C p ( X ) where X is Lindelöf”

Functional separability

A remark on the tightness of products

Convergence in compacta and linear Lindelöfness

Displaying similar documents to “On embeddings into $C_{p} (X)$ where $X$ is Lindelöf”