Histoire des espaces complets

Abstract

SUMMARY. — In the fifth century B.C., it is said, an unknown Pythagorean discovered the irrationality of √2. There begins the long history of the completion of the rationale, to which are tied the names of Euler, Bolzano, Cauchy, Méray, Heine, Cantor, Dedekind, and many others. The next chapter opens with Frécheťs generalization of the Cauchy criterion for metric spaces, Hausdorff's result on the completion of metric spaces, and the introduction of Banach spaces. This leads to the works of Weil, on complete uniform spaces, of Dieudonné, on topological spaces which can receive a complete uniform space structure, and of Grothendieck, on the completion of locally convex topological vector spaces.