Title: On squares of spaces and Fsigma-sets
Author: Arnold W. Miller
Abstract: 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).
Latex2e, 6 pages