Infinitesimal calculus in metric spaces

[摘要] 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 in analysing 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. (c) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2007-12-01

[关键词] arc;differentiability;homotopy;metric space;tangent vector;velocity