On squares of spaces and Fsigma-sets

Arnold W. Miller

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arXiv · math/0404421

On squares of spaces and Fsigma-sets

Arnold W. Miller

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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).

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BibTeX RIS

Arnold W. Miller. 2004-04-22. On squares of spaces and Fsigma-sets. https://arxiv.org/abs/math/0404421

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