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

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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 ≤ T 2 . If X is noncompact and metrizable, then ( ℳ ( X ) , ≤ ) denotes the set of metric extensions of X , where T 1 and T 2 are identified if T 1 ≤ T 2 and T 2 ≤ T 1 , i.e., if there is a homeomorphism of T 1 onto T 2 keeping X pointwise fixed. ( ℳ ( X ) , ≤ ) 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

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In 2008 Juhász and Szentmiklóssy established that for every compact space X there exists a discrete D ⊂ X × 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 ⊂ X × X such that Δ = { ( x , x ) : x ∈ X } ⊂ 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

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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...