Emanuel Sperner

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 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

  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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