On some classes of spaces with the $D$-property

Juan Carlos Martínez

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.

Diagonals and discrete subsets of squares

Dennis Burke, Vladimir Vladimirovich Tkachuk (2013)

Commentationes Mathematicae Universitatis Carolinae

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In 2008 Juhász and Szentmiklóssy established that for every compact space $X$ there exists a discrete $D \subset X \times X$ with $| D | = d (X)$ . We generalize this result in two directions: the first one is to prove that the same holds for any Lindelöf $Σ$ -space $X$ and hence $X^{ω}$ is $d$ -separable. We give an example of a countably compact space $X$ such that $X^{ω}$ is not $d$ -separable. On the other hand, we show that for any Lindelöf $p$ -space $X$ there exists a discrete subset $D \subset X \times X$ such that $Δ = {(x, x) : x \in X} \subset \bar{D}$ ; in particular, the diagonal $Δ$ is a retract of...

Displaying similar documents to “On some classes of spaces with the D -property”

On ℒ -starcompact spaces

Diagonals and discrete subsets of squares

Displaying similar documents to “On some classes of spaces with the $D$ -property”

On $ℒ$ -starcompact spaces