# Borsuk - Ulam theorem proof

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 ?

• The double negative makes your question is hard to parse. Could you edit your question for clarity, please? – Neal Apr 9 '17 at 17:59
• 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 . – Gankedbymom Apr 9 '17 at 18:22