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== Is convexity required? ==
Under "Statement", it is written that the theorem holds only for a convex set. However, under "Notes", it is written that: "For the same reason it holds for every set that is homeomorphic to a closed ball (and therefore also closed, bounded, connected, without holes, etc.).". As far as I know, there are non-convex sets which are homeomorphic to balls. So, does the theorem holds for non-convex set or not?
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)
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