On squares of spaces and Fsigma-sets

Details On squares of spaces and Fsigma-sets On squares of spaces and Fsigma-sets

2004-04-22

arxiv.org/abs/math/0404421v1

Mathematics

Logic

6 pages

Scientific paper

We show that the continuum hypothesis implies there exists a Lindelof space X such that X x X is the union of two metrizable subspaces but X is not metrizable. This gives a consistent solution to a problem of Balogh, Gruenhage, and Tkachuk. The main lemma is that assuming the continuum hypothesis there exist disjoint sets of reals X and Y such that X is Borel concentrated on Y, (i.e., for any Borel set B if Y is contained in B then X-B is countable,) but (X x X - diagonal) is relatively Fsigma in (X x X) U (Y x Y).

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