Knaster–Kuratowski–Mazurkiewicz lemma

The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz.

The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem.

Let ${\displaystyle \Delta _{n-1}}$ be a ${\displaystyle n-1}$-dimensional simplex with n vertices labeled as ${\displaystyle 1,\ldots ,n}$.

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