Science Fair Project Encyclopedia
Emanuel Sperner
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 Salzburg-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.
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details


