Closure-preserving covers in function spaces

David Guerrero Sánchez

Displaying similar documents to “Closure-preserving covers in function spaces”

A game and its relation to netweight and D-spaces

Gary Gruenhage, Paul Szeptycki (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.

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

Oleg Okunev (2009)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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 $ext (C_{p} {(Y)}^{ω}) \leq ext (C_{p} {(X)}^{ω})$ .

A nice class extracted from $C_{p}$ -theory

Vladimir Vladimirovich Tkachuk (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, $ω$ -stable and $ω$ -monolithic. It is also established that any Sokolov compact space $X$ is Fréchet-Urysohn and the space $C_{p} (X)$ is Lindelöf. We prove that any Sokolov space with a $G_{δ}$ -diagonal has a countable network and obtain some cardinality restrictions...

Displaying similar documents to “Closure-preserving covers in function spaces”

A game and its relation to netweight and D-spaces

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

A nice class extracted from C p -theory

A nice class extracted from $C_{p}$ -theory