Emanuel Sperner

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Emanuel Sperner
Emanuel Sperner.jpg
Born (1905-12-09)9 December 1905
Waltdorf, Upper Silesia, German Empire
(now in Poland)
Died 17 March 1980(1980-03-17) (aged 74)
Sulzburg-Laufen, Germany
Nationality German
Alma mater University of Hamburg
Known for Sperner's theorem
Sperner's lemma
Scientific career
Fields Mathematics
Institutions University of Königsberg
University of Bonn
University of Freiburg
University of Hamburg
Doctoral advisor Wilhelm Blaschke
Doctoral students Kurt Leichtweiss
Gerhard Ringel

Emanuel Sperner (9 December 1905 – 31 January 1980) was a German mathematician, best known for two theorems. He was born in Waltdorf (near Neiße, Upper Silesia, now Nysa, Poland), and died in Sulzburg-Laufen, West Germany. He was a student at Carolinum in Nysa and then Hamburg University where his advisor was Wilhelm Blaschke. He was appointed Professor in Königsberg in 1934, and subsequently held posts in a number of universities until 1974.

Sperner's theorem, from 1928, says that the size of an antichain in the power set of an n-set (a Sperner family) is at most the middle binomial coefficient(s).[1] It has several proofs and numerous generalizations, including the Sperner property of a partially ordered set.

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.[2] 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.

Sperner's students included Kurt Leichtweiss and Gerhard Ringel.

References[edit]

  1. ^ Ein Satz über Untermengen einer endlichen Menge. Math. Z. 27 (1928) 544–548.
  2. ^ Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes. Abh. Math. Sem. Hamburg VI (1928) 265–272.

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