A note on transitively $D$-spaces

Liang-Xue Peng

On $k$ -spaces and $k_{R}$ -spaces

Jinjin Li (2005)

Czechoslovak Mathematical Journal

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In this note we study the relation between $k_{R}$ -spaces and $k$ -spaces and prove that a $k_{R}$ -space with a $σ$ -hereditarily closure-preserving $k$ -network consisting of compact subsets is a $k$ -space, and that a $k_{R}$ -space with a point-countable $k$ -network consisting of compact subsets need not be a $k$ -space.

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 “A note on transitively D -spaces”

On k -spaces and k R -spaces

Diagonals and discrete subsets of squares

Displaying similar documents to “A note on transitively $D$ -spaces”

On $k$ -spaces and $k_{R}$ -spaces