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Communication dans un congrès Année : 2023

Taming the infinite: Fréchet and compactness

Résumé

From his first works, Fréchet envisages, in a search for generality, the passage from functions defined on the real line to functions defined on abstract spaces. In order to guarantee the generalization of well-known theorems to the real case, Fréchet proposes various (pre-)topological notions and in particular a definition of compactness which is his own. Our philosophical approach is to show how Fréchet's notion of compactness is a particular way of working with and mastering an infinity linked to his notion of abstract space. We will show that this relation to infinity is different from the one we hear nowadays when we talk about compactness in elementary topology.
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Dates et versions

halshs-04232337, version 1 (07-10-2023)

Identifiants

  • HAL Id : halshs-04232337 , version 1

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Pascal Bertin, Frédéric Jaeck. Taming the infinite: Fréchet and compactness. Maurice Fréchet: Mathematics, the abstract and the concrete, Frédéric Jaëck; Laurent Mazliak, Oct 2023, Paris (IHP), France. ⟨halshs-04232337⟩
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Dernière date de mise à jour le 28/04/2024
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