A remark on the tightness of products

Oleg Okunev

Displaying similar documents to “A remark on the tightness of products”

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

Masami Sakai (1992)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Functional separability

Ronnie Levy, M. Matveev (2010)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Three small results on normal first countable linearly H-closed spaces

Mathieu Baillif (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We use topological consequences of , and proved by other authors to show that normal first countable linearly H-closed spaces with various additional properties are compact in these models.

Displaying similar documents to “A remark on the tightness of products”

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

Functional separability

Three small results on normal first countable linearly H-closed spaces

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