most recent 30 from http://mathoverflow.net 2013-06-19T07:03:24Z http://mathoverflow.net/feeds/question/58223 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58223/what-is-the-origin-of-the-metrization-problem-for-compact-convex-sets Justin Moore 2011-03-12T01:43:16Z 2011-03-12T03:02:14Z

<p>The following is an ``old question in analysis:'' Is it true that every <i>perfectly normal</i> compact convex subset of a locally convex topological vector space is metrizable? Here <i>perfectly normal</i> means Hausdorff plus all closed subsets are a countable intersection of open sets.</p> <p>Who first asked this question? The oldest reference I can locate is a 1972 paper by B. MacGibbon in the Journal of Functional Analysis but it is clear from what is written there that she is reporting progress on a known problem.</p> <p>Of course I am also interested in an answer to this question, but I'm really asking about reference information. I should note that Lopez-Abad and Todorcevic have recently demonstrated that it is consistent with ZFC that there is a counterexample to this problem. The question is whether a positive answer is consistent.</p>