Pseudouniform topologies on $C(X)$ given by ideals

Roberto Pichardo-Mendoza; Angel Tamariz-Mascarúa; Humberto Villegas-Rodríguez

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Displaying similar documents to “Pseudouniform topologies on $C (X)$ given by ideals”

Metrization of function spaces with the Fell topology

Hanbiao Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

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For a Tychonoff space $X$ , let $↓ C_{F} (X)$ be the family of hypographs of all continuous maps from $X$ to $[0, 1]$ endowed with the Fell topology. It is proved that $X$ has a dense separable metrizable locally compact open subset if $↓ C_{F} (X)$ is metrizable. Moreover, for a first-countable space $X$ , $↓ C_{F} (X)$ is metrizable if and only if $X$ itself is a locally compact separable metrizable space. There exists a Tychonoff space $X$ such that $↓ C_{F} (X)$ is metrizable but $X$ is not first-countable.

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

Vladimir Vladimirovich Tkachuk (2005)

Commentationes Mathematicae Universitatis Carolinae

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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...

$𝒫$ -approximable compact spaces

Mihail G. Tkachenko (1991)

Commentationes Mathematicae Universitatis Carolinae

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For every topological property $𝒫$ , we define the class of $𝒫$ -approximable spaces which consists of spaces X having a countable closed cover $γ$ such that the “section” $X (x, γ) = ⋂ {F \in γ : x \in F}$ has the property $𝒫$ for each $x \in X$ . It is shown that every $𝒫$ -approximable compact space has $𝒫$ , if $𝒫$ is one of the following properties: countable tightness, $ℵ_{0}$ -scatteredness with respect to character, $C$ -closedness, sequentiality (the last holds under MA or $2^{ℵ_{0}} < 2^{ℵ_{1}}$ ). Metrizable-approximable spaces are studied: every compact space in...

Displaying similar documents to “Pseudouniform topologies on C ( X ) given by ideals”

Metrization of function spaces with the Fell topology

A nice class extracted from C p -theory

𝒫 -approximable compact spaces

Displaying similar documents to “Pseudouniform topologies on $C (X)$ given by ideals”

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

$𝒫$ -approximable compact spaces