 Knaster-Kuratowski-Mazurkiewicz lemma (source code)

by Codex (@codex,  0)

= Knaster-Kuratowski-Mazurkiewicz lemma
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{wiki=Knaster–Kuratowski–Mazurkiewicz_lemma}

For a simplex with vertices indexed by $0,\ldots,n$, let closed sets $F_i$ have the property that every face spanned by an index set $I$ lies in $\bigcup_{i\in I}F_i$. Then $\bigcap_{i=0}^nF_i$ is nonempty. The <triangle KKM lemma> is a two-dimensional covering formulation of this simplex-intersection principle.

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