Emanuel Sperner

Emanuel Sperner ( born December 9, 1905 in Walt village (now Prusinowice ) in Neisse, Upper Silesia, † 31 January 1980 running, Markgraeflerland ) was a German mathematician who is known for two sets named after him.

Life

He studied at the Albert -Ludwigs- University of Freiburg, and later at the University of Hamburg. He obtained his doctorate under Otto Schreier, where he habilitated as well. His dissertation on November 5, 1928, entitled " New evidence for the invariance of the number of dimensions and the area ." From 1932 to 1934 he was Visiting Professor in China; followed from 1934 to 1943 as a professor at the University of Königsberg, 1943-1945 at the University of Strasbourg, from 1946 to 1949 at the Albert- Ludwigs- University of Freiburg, 1949-1954 at the University of Bonn and from 1954 to 1974 at the University of Hamburg, where he held the office of the rector from 1963 to 1965.

He paused for more visiting professorships and has been involved in building the Mathematical Research Institute Oberwolfach. In 1957 he was president of the German Mathematical Society.

His PhD is one of Gerhard Ringel.

Sets

Two results of Sperner are particularly worthy of mention. Both results are sometimes - especially in the older literature - given the same name as the Spernersche Lemma (English Sperner 's lemma ).

The set of Sperner

This theorem states that an antichain of the power set 2X comprises at most M of an n- element set X elements when M is equal to the largest binomial coefficients of order n.

The Spernersche Lemma

This lemma, as the set of Sperner published in 1928, states that every Sperner coloring of the triangulation of an n- dimensional simplex contains at least one cell that is colored with all the colors. Sperner proved that this lemma provides another proof of a theorem of Lebesgue, with the dimension of a Euclidean space is characterized. Later it was found that this lemma also provides a direct proof of the Brouwer fixed point theorem, which does not require an explicit use of homologies.

Additional Services

From Sperner later time is still his treatment of the parent geometry emphasize with the help of which he had introduced order functions.

Next he gave Otto Schreier's early death out his Lectures on analytic geometry and algebra, which served for decades as a basic textbook for mathematical beginners courses in linear algebra.

Selected works ( from a total of 36 ) of E. Sperner

  • New evidence for the invariance of the number of dimensions and the area. Abh Math Sem Hamburg VI (1928 ) 265-272.
  • A theorem on subsets of a finite set. Math Z. 27 (1928 ) 544-548.
  • About the fixed point free mappings of the plane. Abh math. Se. Hamburg X ( 1934) 1-48.
  • In support of the geometry in the limited level piece. The Konigsberg Learned Society, Math - Naturw writings. Class, ( Halle a d Saale 1938) 121-143.
  • The regulatory function of a geometry. Math Annalen 121 (1949 ) 107-130.
  • Relationships between geometric and algebraic arrangement. Sitzungsber. Heidelberger Akad of Sciences. 1949, 10, Abh, 3-38.
  • Convexity in order functions. Abh Math Sem Hamburg XVI (1949 ), 140-154.
  • A proof of the theorem of Desargues gruppenntheoretischer in the absolute axiomatic. Arch d Math 5 (1954 ), 458-468.
Sperner's lemma Lemma (mathematics) Brouwer fixed-point theorem Karl Rathgen Georg Thilenius Otto Lauffer Wilhelm Blaschke Ernst Cassirer Bruno Snell Karl Schiller Otto Brunner Helmut Thielicke Integrated Authority File
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