2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70945We 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).6 pagesLogicGeneral Topology03E35 54B10 54E35text