A remark on a theorem of Solecki

Petr Holický; Luděk Zajíček; Miroslav Zelený

Displaying similar documents to “A remark on a theorem of Solecki”

Properties of one-point completions of a noncompact metrizable space

Melvin Henriksen, Ludvík Janoš, Grant R. Woods (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

If a metrizable space $X$ is dense in a metrizable space $Y$ , then $Y$ is called a of $X$ . If $T_{1}$ and $T_{2}$ are metric extensions of $X$ and there is a continuous map of $T_{2}$ into $T_{1}$ keeping $X$ pointwise fixed, we write $T_{1} \leq T_{2}$ . If $X$ is noncompact and metrizable, then $(ℳ (X), \leq)$ denotes the set of metric extensions of $X$ , where $T_{1}$ and $T_{2}$ are identified if $T_{1} \leq T_{2}$ and $T_{2} \leq T_{1}$ , i.e., if there is a homeomorphism of $T_{1}$ onto $T_{2}$ keeping $X$ pointwise fixed. $(ℳ (X), \leq)$ is a large complicated poset studied extensively by V. Bel’nov [, Trans. Moscow Math....

Diagonals and discrete subsets of squares

Dennis Burke, Vladimir Vladimirovich Tkachuk (2013)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

The structure of the $σ$ -ideal of $σ$ -porous sets

Miroslav Zelený, Jan Pelant (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show a general method of construction of non- $σ$ -porous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each non- $σ$ -porous Suslin subset of a topologically complete metric space contains a non- $σ$ -porous closed subset. We show also a sufficient condition, which gives that a certain system of compact sets contains a non- $σ$ -porous element. Namely, if we denote the space of all compact subsets of a compact metric space $E$ with the Vietoris...

Displaying similar documents to “A remark on a theorem of Solecki”

Properties of one-point completions of a noncompact metrizable space

Diagonals and discrete subsets of squares

The structure of the σ -ideal of σ -porous sets

The structure of the $σ$ -ideal of $σ$ -porous sets