Kakutani's theorem (geometry)
= Kakutani's theorem (geometry)
{wiki=Kakutani's_theorem_(geometry)}
Kakutani's theorem is a result in the field of geometry and topology, particularly in the study of multi-valued functions and convex sets. It states that if \\( C \\) is a non-empty, compact, convex subset of a Euclidean space, then any continuous map from \\( C \\) into itself that satisfies certain conditions has a fixed point. More specifically, consider a set \\( C \\) that is compact and convex.