Topologie Générale, chapitres 5 à 10 PDF

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Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements. Ce deuxième volume du Livre de Topologie generale, troisième Livre du traite, decrit de nombreux outils fondamentaux en topologie et en analyse, tels que le theorème d Urysohn, le theorème de Baire ou les espaces polonais. Il comprend les chapitres: 1. Groupes à un paramètre; 2. Espaces numeriques et espaces projectifs; 3. Les groupes additifs Rn; 4. Nombres complexes; 5. Utilisation des nombres reels en topologie generale; 6. Espaces fonctionnels. Il contient egalement des notes historiques. Ce volume a ete publie en 1974.

This article is about the group of mathematicians named Nicolas Bourbaki. For the computer scientist, see Nikolaos Bourbakis. Their aim was to reformulate mathematics on an extremely abstract and formal but self-contained basis in a series of books beginning in 1935. In 1934, young French mathematicians from various French universities felt the need to form a group to jointly produce textbooks that they could all use for teaching. André Weil organized the first meeting on 10 December 1934 in the basement of a Parisian grill room, while all participants were attending a conference in Paris.

Accounts of the early days vary, but original documents have now come to light. There was no official status of membership, and at the time the group was quite secretive and also fond of supplying disinformation. The atmosphere in the group can be illustrated by an anecdote told by Laurent Schwartz. Dieudonné regularly and spectacularly threatened to resign unless topics were treated in their logical order, and after a while others played on this for a joke. It is said that Weil’s wife Evelyne supplied Nicolas.