Borsuk-Ulam theorem

From Topospaces
Jump to: navigation, search

This article describes a theorem about spheres

Statement

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