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Talk:Schauder fixed-point theorem

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This is an old revision of this page, as edited by Hut 8.5 (talk | contribs) at 21:56, 22 February 2017 (Hut 8.5 moved page Talk:Schauder fixed point theorem to Talk:Schauder fixed-point theorem: per Fixed-point theorem and similar articles). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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)[reply]

Further updates on http://mathoverflow.net/questions/165853/is-schauders-conjecture-resolved also suggest that Cauty established the proof of Schauder's conjecture in the paper "Un theoreme de Lefschetz-Hopf pour les fonctions a iterees compactes", published online in 2015. --Saung Tadashi (talk) 17:32, 8 November 2016 (UTC)[reply]

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