Talk:Schauder fixed-point theorem
Latest comment: 10 years ago by 134.130.160.208 in topic Gap in the extension to general Hausdorff topological vector spaces by Cauty
The statement of Schaefer's theorem is misleading because it gives the impression that T is linear. If that were the case then the set defined in the statement cannot be bounded (multiply x by any scalar).
Gap in the extension to general Hausdorff topological vector spaces by Cauty
Apparently, in the paper by Cauty (which is quoted as a source of the article), there is a gap. See http://mathoverflow.net/questions/165853/is-schauders-conjecture-resolved. Even the discussion there does not make it completely clear to me whether the general version (without assuming local convexity) is proven or not. I suggest that the article be somewhat rewritten to reflect this. — Preceding unsigned comment added by 134.130.160.208 (talk) 12:46, 20 July 2015 (UTC)