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** Sperner's lemma
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 ).