Pré-Publication, Document De Travail Année : 2007

Infinitesimal calculus in metric spaces

Résumé

We study the possibility of defining tangent vectors to a metric space at a given point and tangent maps to applications from a metric space into another metric space. Such infinitesimal concepts may help analysis in situations in which no obvious differentiable structure is at hand. Some examples are presented; our interest arises from hyperspaces in particular. Our approach is simple and relies on the selection of appropriate curves. Comparisons with other notions are briefly pointed out.

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hal-00175214 , version 1 (27-09-2007)

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  • HAL Id : hal-00175214 , version 1

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Jean-Paul Penot. Infinitesimal calculus in metric spaces. 2007. ⟨hal-00175214⟩
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