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Models for Smooth Infinitesimal Analysis

  • Book
  • © 1991

Overview

Authors:
  1. Ieke Moerdijk

    1. Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

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    You can also search for this author in PubMed   Google Scholar

  2. Gonzalo E. Reyes

    1. Department of Mathematics, University of Montreal, Montreal, Canada

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 1-14

  3. C ∞-Rings

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 15-55

  4. C ∞-Rings as Variable Spaces

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 57-96

  5. Two Archimedean Models for Synthetic Calculus

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 97-131

  6. Cohomology and Integration

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 133-180

  7. Connections on Microlinear Spaces

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 181-237

  8. Models with Invertible Infinitesimals

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 239-292

  9. Smooth Infinitesimal Analysis

    • Ieke Moerdijk, Gonzalo E. Reyes
    Pages 293-344

  10. Back Matter

    Pages 345-399
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

    Ieke Moerdijk

  • Department of Mathematics, University of Montreal, Montreal, Canada

    Gonzalo E. Reyes

Bibliographic Information

  • Book Title: Models for Smooth Infinitesimal Analysis

  • Authors: Ieke Moerdijk, Gonzalo E. Reyes

  • DOI: https://doi.org/10.1007/978-1-4757-4143-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1991

  • Hardcover ISBN: 978-0-387-97489-7Published: 17 December 1990

  • Softcover ISBN: 978-1-4419-3095-8Published: 01 December 2010

  • eBook ISBN: 978-1-4757-4143-8Published: 14 March 2013

  • Edition Number: 1

  • Number of Pages: X, 400

  • Topics: Analysis, Manifolds and Cell Complexes (incl. Diff.Topology)

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