度量切向微积分的元素
Elements for a metric tangential calculus
摘要：
在第一章中介绍的度规喷流是Charles Ehresmann的喷流（一阶）的推广。简而言之，对于一个“好的”映射$f$（被称为在$a$处“可切”），我们定义它在$a$处的度量喷射切线（由所有在$a$处局部Lipschitz的映射和在$a$处与$f$相切的映射组成），称为$f$在$a$处的“切线”，并表示为T $f_a$（$f$的域和余域是度量空间）。此外，在度量喷流T $f_a$的启发性例子的指导下，它与一个在$a$可微的映射$f$相切，这个映射可以用它所包含的唯一连续仿射映射来规范地表示，我们将在第二章中把度量喷流表示的这一性质推广到一个特定的度量环境中，这产生了许多这样的表示的相关例子。
英文摘要：
The metric jets, introduced in the first chapter, generalize the jets (at order one) of Charles Ehresmann. In short, for a "good" map $f$ (said to be "tangentiable" at $a$), we define its metric jet tangent at $a$ (composed of all the maps which are locally lipschitzian at $a$ and tangent to $f$ at $a$) called the "tangential" of $f$ at $a$, and denoted T$f_a$ (the domain and codomain of $f$ being metric spaces). Furthermore, guided by the heuristic example of the metric jet T$f_a$, tangent to a map $f$ differentiable at $a$, which can be canonically represented by the unique continuous affine map it contains, we will extend, in the second chapter, into a specific metric context, this property of representation of a metric jet.This yields a lot of relevant examples of such representations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
