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Displaying similar documents to “Universal meager F σ -sets in locally compact manifolds”

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....

A semifilter approach to selection principles

Lubomyr Zdomsky (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal 𝔤 is a lower bound of the additivity number of the σ -ideal generated by Menger subspaces of the Baire space, and under 𝔲 < 𝔤 every subset X of the real line with the property Split ( Λ , Λ ) is Hurewicz, and thus it is consistent with ZFC that the property Split ( Λ , Λ ) is preserved by unions of less than 𝔟 subsets of the real line.