当代无穷小连续统理论及其19世纪末和20世纪初的先驱
Contemporary Infinitesimalist Theories of Continua and their late 19th- and early 20th-century forerunners
摘要：
本文的目的是提供一个历史的概述，一些当代的无穷小替代康托-戴德金理论的连续统。在这些理论中，我们将考虑的是那些出现在非标准分析，幂零无穷小方法的部分微分几何和理论的超实数。由于这些理论都植根于19世纪末和20世纪初的代数，几何和分析无穷小理论，我们也将提供后者的理论和他们的一些关系，当代的概述。
英文摘要：
The purpose of this paper is to provide a historical overview of some of the contemporary infinitesimalist alternatives to the Cantor-Dedekind theory of continua. Among the theories we will consider are those that emerge from nonstandard analysis, nilpotent infinitesimalist approaches to portions of differential geometry and the theory of surreal numbers. Since these theories have roots in the algebraic, geometric and analytic infinitesimalist theories of the late nineteenth and early twentieth centuries, we will also provide overviews of the latter theories and some of their relations to the contemporary ones.
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。
