Borsuk-Ulam theorem

This article describes a theorem about spheres

Statement

Let $S^m$ denote the $m$-dimensional sphere (embedded in ${\mathbb{R}}^{m+1}$) and ${\mathbb{R}}^m$ denote $m$-dimensional Euclidean space. Then, given any continuous map $f:S^m\to {\mathbb{R}}^m$, there is a point $x\in S^m$ such that $f(x)=f(-x)$.