The following is an ``old question in analysis:''
Is it true that every *perfectly normal* compact convex subset of a locally convex topological vector space is metrizable?
Here *perfectly normal* means Hausdorff plus all closed subsets are a countable intersection of open sets.

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.

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.

normal(compact convex) set? – Joseph O'Rourke Mar 12 '11 at 2:34