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＜電子ブック＞
Models for Smooth Infinitesimal Analysis / by Ieke Moerdijk, Gonzalo E. Reyes

版	1st ed. 1991.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1991
本文言語	英語
大きさ	X, 400 p : online resource
著者標目	*Moerdijk, Ieke author Reyes, Gonzalo E author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Manifolds (Mathematics) FREE:Analysis FREE:Manifolds and Cell Complexes
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4757-4143-8

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