Talk:Schauder fixed-point theorem

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)