Borsuk-Ulam Theorem

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Theorem

Let $n$ be a positive integer.

Let $f: \mathbb S^n \to \R^n$ be a continuous mapping from an $n$-sphere to $\R^n$.


Then there exists $x \in \mathbb S^n$ such that $f \left({x}\right) = f \left({-x}\right)$.


Proof


Source of Name

This entry was named for Karol Borsuk and Stanisław Marcin Ulam.