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!

  • $\begingroup$ See: mathoverflow.net/questions/22294/… . $\endgroup$ – Justin Young May 24 '13 at 13:06
  • $\begingroup$ @Rahman Have you get the version of Kakutani fixed point theorem in algebraic topology? $\endgroup$ – Yan kai Apr 15 '14 at 3:52
  • $\begingroup$ I just stumbled across this thread while browsing unanswered game theory questions, but I actually just posted a proof to the linked overflow post which might be of the flavor you're after. $\endgroup$ – Pete Caradonna Feb 26 '17 at 20:45

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