Displaying similar documents to “Two point sets with additional properties”

On nonmeasurable images

Robert Rałowski, Szymon Żeberski (2010)

Czechoslovak Mathematical Journal

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Let ( X , 𝕀 ) be a Polish ideal space and let T be any set. We show that under some conditions on a relation R ⊆ T 2 × X it is possible to find a set A ⊆ T such that R ( A 2 ) is completely 𝕀 -nonmeasurable, i.e, it is 𝕀 -nonmeasurable in every positive Borel set. We also obtain such a set A ⊆ T simultaneously for continuum many relations ( R α ) α < 2 ω . Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.

Completely nonmeasurable unions

Robert Rałowski, Szymon Żeberski (2010)

Open Mathematics

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Assume that no cardinal κ < 2ω is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal of subsets of κ such that the Boolean algebra P(κ)/ satisfies c.c.c.). We show that for a metrizable separable space X and a proper c.c.c. σ-ideal II of subsets of X that has a Borel base, each point-finite cover ⊆ 𝕀 of X contains uncountably many pairwise disjoint subfamilies , with 𝕀 -Bernstein unions ∪ (a subset A ⊆ X is 𝕀 -Bernstein if A and X A meet each Borel 𝕀 -positive...

Some topological properties of ω -covering sets

Andrzej Nowik (2000)

Czechoslovak Mathematical Journal

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We prove the following theorems: There exists an ω -covering with the property s 0 . Under c o v ( 𝒩 ) = there exists X such that ∀ B ∈ ℬ o r [ B ∩ X is not an ω -covering or X ∖ B is not an ω -covering]. Also we characterize the property of being an ω -covering.