Models for Smooth Infinitesimal Analysis / Edition 1

by Ieke Moerdijk, Gonzalo E. Reyes

Overview

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.

Product Details

ISBN-13:	9781441930958
Publisher:	Springer New York
Publication date:	12/01/2010
Edition description:	Softcover reprint of hardcover 1st ed. 1991
Pages:	400
Sales rank:	913,168
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

I C?-Rings.- II C?-Rings as Variable Spaces.- III Two Archimedean Models for Synthetic Calculus.- IV Cohomology and Integration.- V Connections on Microlinear Spaces.- VI Models with Invertible Infinitesimals.- VII Smooth Infinitesimal Analysis.- Appendix 1: Sheaves and Forcing.- 1 Sites.- 2 Sheaves.- 3 Forcing.- Appendix 2: A survey of models.- Appendix 3: The integration axiom.- Appendix 4: The amazing right adjoint.- Appendix 5: Comments, References and Further Developments.- Index of symbols.

Editorial Reviews

Explains infinitesimals and infinitely large integers, as they were used before their elimination by the set-theoretic trend in mathematics. The explanation doesn't go against this trend, but gives a consistent reinterpretation of infinitesimals in a set-theoretic context, through the use of sheaf theory. The main concern is to show that synthetic differential geometry has a clear and direct relation to the classical theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews