Two point sets with additional properties

Marek Bienias; Szymon Głąb; Robert Rałowski; Szymon Żeberski

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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 $R \subseteq T^{2} \times X$ it is possible to find a set $A \subseteq T$ 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 $A \subseteq T$ 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 $\forall_{B \in ℬ o r} [B \cap X$ is not an $ω$ -covering or $X ∖ B$ is not an $ω$ -covering]. Also we characterize the property of being an $ω$ -covering.

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

On nonmeasurable images

Completely nonmeasurable unions

Some topological properties of ω -covering sets

Some topological properties of $ω$ -covering sets