The Borsuk - Ulam says the following : For any continuous map $g : S^{n} \to \mathbb{R}^n$ there exist a point $x \in S^{n}$ such that $g(x) = g(-x)$ I doubt that It can't be proved by using the knowledge about homology groups likes Brouwer fixed point . Can anyone help me ?

  • $\begingroup$ The double negative makes your question is hard to parse. Could you edit your question for clarity, please? $\endgroup$ – Neal Apr 9 '17 at 17:59
  • $\begingroup$ You know the Brouwer fixed point can be proved by the degree of continuous map on $S^{n}$ so I try to find a solution for BUT just use homology group ( I'm learning homology groups ) . But I know that this theorem relates to cohomology or something higher . $\endgroup$ – Gankedbymom Apr 9 '17 at 18:22

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