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@sesiru8 ベクトル束の無限次元版という文脈でいうと Lang の本（https://t.co/XpP0PQUrkW）には Banach束についての記述があります． （ちなみにこの本は無限次元多様体（Banach manifold）で議論を進めています） 一部だけですが，https://t.co/GOTT5GJhA8 でプレビューも見れます．
Fundamentals of Differential Geometry
Overview of attention for book
Table of Contents
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Altmetric BadgeBook Overview
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Altmetric BadgeChapter 1 Differential Calculus
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Altmetric BadgeChapter 2 Manifolds
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Altmetric BadgeChapter 3 Vector Bundles
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Altmetric BadgeChapter 4 Vector Fields and Differential Equations
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Altmetric BadgeChapter 5 Operations on Vector Fields and Differential Forms
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Altmetric BadgeChapter 6 The Theorem of Frobenius
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Altmetric BadgeChapter 7 Metrics
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Altmetric BadgeChapter 8 Covariant Derivatives and Geodesics
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Altmetric BadgeChapter 9 Curvature
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Altmetric BadgeChapter 10 Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle
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Altmetric BadgeChapter 11 Curvature and the Variation Formula
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Altmetric BadgeChapter 12 An Example of Seminegative Curvature
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Altmetric BadgeChapter 13 Automorphisms and Symmetries
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Altmetric BadgeChapter 14 Immersions and Submersions
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Altmetric BadgeChapter 15 Volume Forms
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Altmetric BadgeChapter 16 Integration of Differential Forms
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Altmetric BadgeChapter 17 Stokes’ Theorem
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Altmetric BadgeChapter 18 Applications of Stokes’ Theorem