Emanuel Sperner

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Emanuel Sperner (9 December 1905 - 31 January 1980) was a German mathematician, best known for two theorems. He was born in Waltdorf (near Nysa, now in Poland), and died in Sulzburg-Laufen. He was a student at Hamburg University. He was appointed Professor in Königsberg in 1934, and subsequently held posts in a number of universities until 1974.

The Sperner theorem, from 1927, says that the number of antichains in the power set of an n-set is at most the middle binomial coefficient(s). It has several proofs and numerous generalizations.

Sperner's lemma, from 1924, states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors. It was proven by Sperner to provide an alternate proof of a theorem of Lebesgue characterizing dimensionality of Euclidean spaces. It was later noticed that this lemma provides a direct proof of the Brouwer fixed-point theorem without explicit use of homology.