Anmerkungen:
Includes bibliographical references and index
This edition previously issued in print: 2018
Zielgruppe - Audience: Specialized
Beschreibung:
Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts