As Kakutani fixed point theorem is a genral case of Brouwer fixed point theorem, and one can read the proof from homotopy theory books. I wonder if there is any proof for the Kakutani using homotopy theory or if it has at least some applications in algebraic topology! you can refer me to some refernces.. thanks!
2026-02-23 02:28:52.1771813732
algebraic or homotopical proof for Kakutani fixed point theorem
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