Models for Smooth Infinitesimal Analysis - Hardcover

Moerdijk, Ieke; Reyes, Gonzalo E.

Hardcover

ISBN 10: 038797489X ISBN 13: 9780387974897

Publisher: Springer, 1990

Synopsis

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.

About this title

Synopsis

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

Edition details

• Publisher: Springer
• Publication date: 1990
• Language: English
• ISBN 10: 038797489X
• ISBN 13: 9780387974897
• Binding: Hardcover
• Number of pages: 410