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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. <small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/134.130.160.208|134.130.160.208]] ([[User talk:134.130.160.208|talk]]) 12:46, 20 July 2015 (UTC)</small><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
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 "[https://www.degruyter.com/abstract/j/crll.ahead-of-print/crelle-2014-0134/crelle-2014-0134.xml Un theoreme de Lefschetz-Hopf pour les fonctions a iterees compactes]", published online in 2015. --[[User:Saung Tadashi|Saung Tadashi]] ([[User talk:Saung Tadashi|talk]]) 17:32, 8 November 2016 (UTC)
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