Models for Smooth Infinitesimal Analysis

Ieke Moerdijk

ISBN 10: 038797489X / ISBN 13: 9780387974897

Editore: Springer New York Dez 1990, 1990

Riguardo questo articolo

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.

Codice articolo 9780387974897

Dati bibliografici

• Titolo: Models for Smooth Infinitesimal Analysis
• Editore: Springer New York Dez 1990
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 038797489X
• ISBN 13: 9780387974897
• Rilegatura: Buch
• Condizione: Neu

Descrizione articolo

Riassunto

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.

Contenuti

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.