Models for Smooth Infinitesimal Analysis

Ieke Moerdijk

ISBN 10: 038797489X / ISBN 13: 9780387974897

Published by Springer New York Dez 1990, 1990

About this Item

Neuware - 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.

Seller Inventory # 9780387974897

Bibliographic Details

• Title: Models for Smooth Infinitesimal Analysis
• Publisher: Springer New York Dez 1990
• Publication Date: 1990
• Language: English
• ISBN 10: 038797489X
• ISBN 13: 9780387974897
• Binding: Buch
• Condition: Neu

About this title

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.

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