Models for Smooth Infinitesimal Analysis

Ieke Moerdijk, Gonzalo E. Reyes (Autoren)

Buch | Softcover

400 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1991
Springer-Verlag New York Inc.
978-1-4419-3095-8 (ISBN)

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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.

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.

Erscheint lt. Verlag	1.12.2010
Zusatzinfo	X, 400 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4419-3095-7 / 1441930957
ISBN-13	978-1-4419-3095-8 / 9781441930958
Zustand	Neuware