Theorem Brouwer Fixed Point Theorem
theorem staged

Brouwer Fixed Point Theorem

Let $C$ be a nonempty convex compact subset of a finite-dimensional Euclidean space. Every continuous function $$ f:C\to C $$ has a fixed point.

References

  • [MFoGT, Thm. 4.11.4] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Brouwer fixed point theorem for compact convex subsets of finite-dimensional Euclidean space.

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