Maurice René Fréchet

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Maurice René Fréchet

Maurice René Fréchet (born September 2, 1878 in Maligny , Yonne department ; † June 4, 1973 in Paris ) was a French mathematician who wrote fundamental work in functional analysis .


Fréchet went to school at the Lycée Buffon in Paris, where Jacques Hadamard was his teacher and promoted his mathematical talent. After studying (1900–1903) at the École normal supérieure , he received his doctorate there in 1906 with Hadamard (Sur quelques points du calcul fonctionnel). Around this time he also edited lectures by Émile Borel on real functions and by Hadamard on calculus of variations for publication and also made contacts with American mathematicians such as Edwin Wilson . 1907/1908 he was a mathematics teacher at the grammar school (Lycée) in Besançon , 1908/1909 in Nantes and from 1910 to 1919 professor of mechanics at the Faculté des Sciences in Poitiers . Originally he wanted to teach 1914/1915 at the University of Illinois in Urbana, which was prevented by the First World War, during which he did military service as a liaison officer to the English. After the war he was involved in setting up the now French university in Strasbourg , where he was professor of higher analysis and director of the mathematical institute from 1919 to 1927. During this time he also organized the International Congress of Mathematicians in Strasbourg in 1920. With the support of Emile Borel, he went to Paris from 1928, where he was Maître de Recherches at the École des Hautes-Études, then professor at the Faculté des Sciences and, from 1929, additionally professor of mechanics and analysis at the Ecole Normale Superieure. In 1948 he retired.

In 1956, after several unsuccessful attempts, he was elected as a full member of the Académie des sciences ; since June 30, 1952 he was already a corresponding member. In 1948 he became a member of the Royal Society of Edinburgh and in 1929 the Polish Academy of Sciences . He was an honorary member of the Portuguese Mathematical Society and gave lectures in Lisbon in 1942. In 1935 he was president of the Société Mathématique de France .

He had been married since 1908 and had four children.

He was in correspondence with many important mathematicians, including the Russian mathematicians Nikolai Nikolajewitsch Lusin , Pawel Alexandrow and Urysohn , with Frigyes Riesz , LEJ Brouwer and with Polish mathematicians such as Waclaw Sierpinski and Kazimierz Kuratowski .


In functional analysis he introduced metric spaces in his doctoral thesis in 1906 and laid the foundations of topology in his search for abstraction in the works of Vito Volterra , Cesare Arzelà , Jacques Hadamard and Georg Cantor . The name metric space does not come from him, however, but from Felix Hausdorff . Fréchet also introduced the terms compactness and separability in his dissertation .

Fréchet also introduced the concepts of uniform convergence and uniform continuity . It was also Fréchet who was the first to use the term Banach space in 1928 , referring to the subsequent spaces as Banach spaces.

During his time in Paris from 1928 onwards, he turned to statistics and probability theory, on which he had already given lectures in Strasbourg.

In 1936 he gave a plenary lecture at the International Congress of Mathematicians in Oslo (Mélanges mathématiques) and also in Bologna in 1928 (L'analyse générale et les espaces abstraits).

His name is u. a. associated with the following terms:

In 2001 the asteroid (21537) Fréchet was named after him.


  • Les espaces abstraits et leur théorie considérée comme introduction à l'analyse générale , Paris, Gauthier-Villars, 1928
  • L'arithmétique de l'infini , Paris, Hermann 1934
  • Récherches théoriques modern sur la théorie des probabilités , 2 volumes, Paris, Gauthier-Villars 1950, 1952
  • with Ky Fan Introduction à la topologie combinatoire , 1946 (English translation Introduction to combinatorial topology , Boston 1967)
  • Pages choisies d'analysis générale , Paris, Gauthier-Villars, 1953
  • Les mathématiques et le concret , Presse Universitaire de France, 1955
  • with Maurice Halbwachs Le calcul des probabilités à la portée de tous , Paris, Dunod 1924. Reissued by Presses Universitaires de Strasbourg, 2019.


  • Helmut Goldmann: Uniform Fréchet algebras . North-Holland, Amsterdam 1990, ISBN 0-444-88488-2 .
  • Norman M. Martin: Close spaces and logic . Kluwer, Dordrecht 1996, ISBN 0-7923-4110-4 .

Web links

Individual evidence

  1. Published in Rendicondi Circolo Matematico di Palermo, Volume 22, 1906, pp. 1-74.
  2. ^ List of members since 1666: Letter F. Académie des sciences, accessed on November 16, 2019 (French).
  3. ^ Hausdorff Fundamentals of Set Theory , Leipzig, 1914.
  4. ^ Pietsch History of Banach spaces and linear operators , Birkhäuser, 2007, p. 7.