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 groundbreaking work in the functional analysis.

Life

Fréchet was at the Lycée Buffon in Paris to school where Hadamard was his teacher and his mathematical talent promoted. After his studies ( 1900-1903 ) at the École normale supérieure, he received his doctorate in 1906 at Hadamard ( Sur quelque points you calcul fonctionelle ). Around this time he also worked lectures by Émile Borel real functions and Hadamard via calculus of variations for the publication and established contacts with American mathematicians such as Edwin Wilson. 1907/1908 he was a math teacher at the high school ( Lycée ) in Besancon, 1908/1909 in Nantes, 1910-1919 Professor of Mechanics at the Faculté des Sciences in Poitiers. Originally, he wanted 1914/1915 to teach at the University of Illinois in Urbana, which was prevented by the First World War, during which he performed military service as a liaison officer to the British. After the war he was involved in the construction of the French now become University of Strasbourg, where he was from 1919 to 1927 Professor of Higher Analysis and director of the Mathematical Institute. During this time he also organized the International Congress of Mathematicians 1920 in Strasbourg. With the support of Emile Borel in 1928 he went to Paris, where he was Maitre de Recherches at the École des Hautes Études -, then a professor at the Faculté des Sciences, and from 1929 also professor of Mechanics and Analysis at the Ecole Normale Superieure. In 1948, he went into retirement.

In 1956 he was elected after several unsuccessful previous attempts in the Académie des sciences. 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 in 1942 and held lectures in Lisbon.

He was married in 1908 and had four children.

He was in correspondence with many eminent mathematicians, among others, the Russian mathematicians Nikolai Nikolaevich Luzin, Pavel Aleksandrov and Urysohn, Frigyes Riesz with, LEJ Brouwer, and with Polish mathematicians such as Waclaw Sierpinski and Kazimierz Kuratowski.

Work

In the functional analysis, he led in 1906 in his PhD thesis, the metric spaces and laid foundation stones of the topology, in his search for abstraction of the works of Vito Volterra, Cesare Arzela, Jacques Hadamard and Georg Cantor. The name of metric space but is not by him but by Felix Hausdorff. Fréchet resulted in his dissertation also the concepts of compactness and separability.

Fréchet also introduced the concepts of uniform convergence and uniform continuity. It was also Fréchet, who used the term first in 1928 as a Banach space, which he then described the sequence spaces as Banach spaces.

During his time in Paris from 1928, he turned to statistics and probability theory, about which he had already lectured 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'analyze generale et les espaces abstraits ).

His name is, inter alia, linked to the following terms:

• Fréchet derivative
• Fréchet filter
• Fréchet metric
• Fréchet space
• Fréchet distribution

Writings

• Les espaces abstraits et leur théorie comme considérée introduction à l' analyze générale, Paris, Gauthier -Villars, 1928
• L' arithmétique de l' infini, Paris, Hermann, 1934
• Recherches sur la théorie modern théoretiques of probabilites, 2 volumes, Paris, Gauthier -Villars 1950, 1952
• With Ky Fan Introduction à la topology Combinatoire, 1946 (English translation Introduction to combinatorial topology, Boston 1967)
• Pages choisies d'analyze générale, Paris, Gauthier -Villars, 1953
• Les Mathématiques et le concret, press Universitaire de France, 1955
• With other Le calcul of the probabilites à la portée de tous, Paris, Dunod 1924