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AuthorMoerdijk, Ieke. author
TitleModels for Smooth Infinitesimal Analysis [electronic resource] / by Ieke Moerdijk, Gonzalo E. Reyes
ImprintNew York, NY : Springer New York : Imprint: Springer, 1991
Connect tohttp://dx.doi.org/10.1007/978-1-4757-4143-8
Descript X, 400 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Manifolds (Mathematics) Complex manifolds Mathematics Analysis Manifolds and Cell Complexes (incl. Diff.Topology)



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