On the extent of separable, locally compact, selectively (a)-spaces

Samuel G. da Silva

Displaying similar documents to “On the extent of separable, locally compact, selectively (a)-spaces”

Weak extent in normal spaces

Ronnie Levy, Mikhail Matveev (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

If $X$ is a space, then the $we (X)$ of $X$ is the cardinal $min {α :$ If $𝒰$ is an open cover of $X$ , then there exists $A \subseteq X$ such that $| A | = α$ and $St (A, 𝒰) = X}$ . In this note, we show that if $X$ is a normal space such that $| X | = 𝔠$ and $we (X) = ω$ , then $X$ does not have a closed discrete subset of cardinality $𝔠$ . We show that this result cannot be strengthened in ZFC to get that the extent of $X$ is smaller than $𝔠$ , even if the condition that $we (X) = ω$ is replaced by the stronger condition that $X$ is separable.

The Banach algebra of continuous bounded functions with separable support

M. R. Koushesh (2012)

Studia Mathematica

Similarity:

We prove a commutative Gelfand-Naimark type theorem, by showing that the set $C_{s} (X)$ of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if...

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

Similarity:

In this note we first give a summary that on property of a remainder of a non-locally compact topological group $G$ in a compactification $b G$ makes the remainder and the topological group $G$ all separable and metrizable. If a non-locally compact topological group $G$ has a compactification $b G$ such that the remainder $b G ∖ G$ of $G$ belongs to $𝒫$ , then $G$ and $b G ∖ G$ are separable and metrizable, where $𝒫$ is a class of spaces which satisfies the following conditions: (1) if $X \in 𝒫$ , then every compact subset of the...

In search for Lindelöf $C_{p}$ ’s

Raushan Z. Buzyakova (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_{p} (X)$ is Lindelöf. This result is used to construct an example of a countably compact space $X$ such that the extent of $C_{p} (X)$ is less than the Lindelöf number of $C_{p} (X)$ . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.

Displaying similar documents to “On the extent of separable, locally compact, selectively (a)-spaces”

Weak extent in normal spaces

The Banach algebra of continuous bounded functions with separable support

A note on topological groups and their remainders

In search for Lindelöf C p ’s

In search for Lindelöf $C_{p}$ ’s