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Maurice Fréchet (September 2, 1878 – June 4, 1973) was a French mathematician.

In 1906, he introduced the concept of abstract space, including metric space, topological space and vector space and was also one of the founders of functional analysis. He was a student of Jacques Hadamard at École Normale Supérieure.

He spent nine years at the University of Poititers as a professor of mechanics. He later moved to the University of Strasbourg where he served as a professor of higher calculus, where he spent 7 years. In 1928 he joined the University of Paris, taking on various professorial posts.

As noted above, his major contribution is the introduction of abstract spaces, where he applied the intuitive Euclidean geometry to form abstract relationships between the elements of the space. Particularly important are his generalisations of the concept of limit, continuity, convergent sequence and Cauchy sequence to the abstract setting. This led him to coin the term compact space. These new concepts were incredibly successful and are today considered to be the iron repertoire of any good analysis course. The entire field of functional analysis has emerged from Fréchet's ideas.

His major works are, in chronological order:
- Les Espaces abstraits, 1928 (Abstract spaces)
- Récherches théoriques modernes sur la théorie des probabilités, 1937-1938 (Modern theoretical research in the theory of probability)
- Les Probabilités associées à un système d'évenements compatibles et dependants, 1939-1943 (The Probabilities Associated with a System of Compatible and Dependent Events)
- Pages choisies d'analyse générale 1953 (Selected Pages of General Analysis)
- Les Mathématiques et le concret 1955 (Mathematics and the concrete)

The Fréchet metric is a metric function upon an infinite cartesian product of metric spaces <X₁,d₁>,<X₂,d₂>..., defined by: ${\displaystyle d(x,y)=\sum {\frac {1}{2^{n}}}{\frac {d_{n}(x_{n},y_{n})}{1+d_{n}(x_{n},y_{n})}}}$

See also

• Fréchet space
• Fréchet-Urysohn space
• Fréchet derivative
• Fréchet distribution

References

• O'Connor, John J.; Robertson, Edmund F., "René Maurice Fréchet", MacTutor History of Mathematics Archive, University of St Andrews
• René Maurice Fréchet at the Mathematics Genealogy Project

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