An answer to a question of Arhangel'skii

Henryk Michalewski

Displaying similar documents to “An answer to a question of Arhangel'skii”

On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces

Oleg Okunev (2009)

Commentationes Mathematicae Universitatis Carolinae

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We study relations between the Lindelöf property in the spaces of continuous functions with the topology of pointwise convergence over a Tychonoff space and over its subspaces. We prove, in particular, the following: a) if $C_{p} (X)$ is Lindelöf, $Y = X \cup {p}$ , and the point $p$ has countable character in $Y$ , then $C_{p} (Y)$ is Lindelöf; b) if $Y$ is a cozero subspace of a Tychonoff space $X$ , then $l (C_{p} {(Y)}^{ω}) \leq l (C_{p} {(X)}^{ω})$ and $ext (C_{p} {(Y)}^{ω}) \leq ext (C_{p} {(X)}^{ω})$ .

On embeddings into $C_{p} (X)$ where $X$ is Lindelöf

Masami Sakai (1992)

Commentationes Mathematicae Universitatis Carolinae

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A.V. Arkhangel’skii asked that, is it true that every space $Y$ of countable tightness is homeomorphic to a subspace (to a closed subspace) of $C_{p} (X)$ where $X$ is Lindelöf? $C_{p} (X)$ denotes the space of all continuous real-valued functions on a space $X$ with the topology of pointwise convergence. In this note we show that the two arrows space is a counterexample for the problem by showing that every separable compact linearly ordered topological space is second countable if it is homeomorphic to a subspace...

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 $𝔠$ .

Displaying similar documents to “An answer to a question of Arhangel'skii”

On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces

On embeddings into C p ( X ) where X is Lindelöf

A remark on the tightness of products

On embeddings into $C_{p} (X)$ where $X$ is Lindelöf