Universally meager sets


Piotr Zakrzewski

6 pages; Proc. Amer. Math. Soc., to appear.

We study category counterparts of the notion of a universal measure zero set of reals.

We say that a subset A of R is universally meager, if every Borel isomorphic image of A is meager in R. We give various equivalent definitions emphasizing analogies with the universally null sets of reals.

In particular, two problems emerging from an earlier work of Grzegorek are solved.

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