Suppose that K is a nonempty compact convex set in R^n. If f:K->K is not continuous, then f will not have any fixed point.(adsbygoogle = window.adsbygoogle || []).push({});

I believe this statement is false, but I cannot think of a function(not continuous) that maps a compact convex set to another compact convex set.

any tips would be appreciated

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# Convexity and fixed points

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