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It could be good to show an example of a non-convex set on which the result does not hold. --[[User:Erel Segal|Erel Segal]] ([[User talk:Erel Segal|talk]]) 06:31, 19 December 2014 (UTC)
* For a ''compact'' convex set, which that it is homeomorphic to a ball. So e.g. an annulus is compact non-convex, and a rotation maps it to itself without fixpoint. --[[Special:Contributions/206.214.242.230|206.214.242.230]] ([[User talk:206.214.242.230|talk]]) 18:30, 23 January 2015 (UTC)
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