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On squares of spaces and Fsigma-sets | | Arnold W. Miller
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22 Apr 2004 | | Subject: | Logic; General Topology MSC-class: 03E35 54B10 54E35 | math.LO math.GN | | 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). | | Source: | arXiv, math.LO/0404421 | | Services: | Forum | Review | PDF | Favorites | |
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