×

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
PDF BibTeX XML Cite