Infinitesimal calculus in metric spaces

Jean-Paul Penot (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

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.

Mots clés: arc; Differentiability; homotopy; metric space; tangent vector; velocity

Domaines: Géométrie métrique [math.MG]

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