## Certain measure zero, first category sets.(English)Zbl 0761.28001

The author deals with sets of measure zero, meager sets, and subsets of the reals which contain a translated copy of every countable subset of $$R$$. Under $$2^{\aleph_ 0}=\aleph_ 2$$ and the existence of a Sierpinski set of size $$\aleph_ 2$$ he proves that there exists a meager set which contains a translated copy of every set of size smaller than $$\aleph_ 2$$.

### MSC:

 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets