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A note on G δ ideals of compact sets

Maya Saran (2009)

Commentationes Mathematicae Universitatis Carolinae

Solecki has shown that a broad natural class of G δ ideals of compact sets can be represented through the ideal of nowhere dense subsets of a closed subset of the hyperspace of compact sets. In this note we show that the closed subset in this representation can be taken to be closed upwards.

A note on intersections of non-Haar null sets

Eva Matoušková, Miroslav Zelený (2003)

Colloquium Mathematicae

We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.

A problem with almost everywhere equality

Piotr Niemiec (2012)

Annales Polonici Mathematici

A topological space Y is said to have (AEEP) if the following condition is satisfied: Whenever (X,) is a measurable space and f,g: X → Y are two measurable functions, then the set Δ(f,g) = x ∈ X: f(x) = g(x) is a member of . It is shown that a metrizable space Y has (AEEP) iff the cardinality of Y is not greater than 2 .

A Q -linear automorphism of the reals with non-measurable graph

Stephen Scheinberg (2019)

Commentationes Mathematicae Universitatis Carolinae

This note contains a proof of the existence of a one-to-one function Θ of onto itself with the following properties: Θ is a rational-linear automorphism of , and the graph of Θ is a non-measurable subset of the plane.

A remark on a theorem of Solecki

Petr Holický, Luděk Zajíček, Miroslav Zelený (2005)

Commentationes Mathematicae Universitatis Carolinae

S. Solecki proved that if is a system of closed subsets of a complete separable metric space X , then each Suslin set S X which cannot be covered by countably many members of contains a G δ set which cannot be covered by countably many members of . We show that the assumption of separability of X cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the σ -ideal generated by is locally determined. Using Solecki’s arguments, our result can be used...

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