Models for Smooth Infinitesimal Analysis

Moerdijk, Ieke; Reyes, Gonzalo E.

The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.

Details

Published by: Springer

Publication Date: 2010-12-01

Format: Paperback

ISBN-13: 9781441930958

DOI: 10.1007/978-1-4757-4143-8

Dimensions: 235cm x155cm

Pages: 400