On $D$-property of strong $\Sigma $ spaces

Raushan Z. Buzyakova

Weak extent in normal spaces

Ronnie Levy, Mikhail Matveev (2005)

Commentationes Mathematicae Universitatis Carolinae

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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.

On $ℒ$ -starcompact spaces

Yan-Kui Song (2006)

Czechoslovak Mathematical Journal

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A space $X$ is $ℒ$ -starcompact if for every open cover $𝒰$ of $X,$ there exists a Lindelöf subset $L$ of $X$ such that $S t (L, 𝒰) = X .$ We clarify the relations between $ℒ$ -starcompact spaces and other related spaces and investigate topological properties of $ℒ$ -starcompact spaces. A question of Hiremath is answered.

Displaying similar documents to “On D -property of strong Σ spaces”

Weak extent in normal spaces

On ℒ -starcompact spaces

Displaying similar documents to “On $D$ -property of strong $Σ$ spaces”

On $ℒ$ -starcompact spaces