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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