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** Sperner's lemma

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## Some Related Sentences

** and lemma

__**__Zorn's

__lemma__: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

__**__Tukey's

__lemma__: Every non-empty collection of finite character has a maximal element with respect to inclusion.

Sperner's and lemma

__Sperner's__

__lemma__, from 1928, states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.

In mathematics,

__Sperner's____lemma__is a combinatorial analog of the Brouwer fixed point theorem, which follows from it.__Sperner's__

__lemma__states that every Sperner coloring ( described below ) of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.

By contrast, the Brouwer fixed-point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point ( See also

__Sperner's____lemma__).0.071 seconds.