| Description |
1 online resource (492 p.) |
| Series |
Chapman and Hall/CRC Monographs and Research Notes in Mathematics Series |
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Chapman and Hall/CRC Monographs and Research Notes in Mathematics Series
|
| Contents |
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Authors -- Acknowledgements -- List of Figures -- 1. Preliminaries -- 1.1. Banach Spaces -- 1.2. Examples of Banach Spaces -- 1.3. Dual Spaces -- 1.4. Properties -- 1.5. Derivatives in Banach Spaces -- 1.6. Ordinary Differential Equations -- 1.7. Banach Manifolds -- 1.8. Banach Manifold Structures on Sets of Maps -- 1.9. Banach Submanifolds -- 1.10. Banach-Lie Groups and Lie Algebras -- 1.11. Banach Vector Bundles -- 1.12. Jets of Sections of a Vector Bundle -- 1.13. Notes |
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2. Banach-Lie Structures -- 2.1. Linear Tensor Structures -- 2.2. Banach G-Structures and Tensor Structures -- 2.3. Examples of Tensor Structures on a Banach Bundle -- 2.4. Examples of Integrable Tensor Structures on a Banach Manifold -- 2.5. Darboux Theorem for Symplectic Forms on a Banach Manifold -- 2.6. Notes -- 3. Convenient Structures -- 3.1. Locally Convex Topological Vector Spaces -- 3.2. Differential Calculus on Locally Convex Topological Vector Spaces -- 3.3. Convenient Calculus -- 3.4. Convenient Manifolds -- 3.5. Tangent Vectors -- 3.6. Tangent Mappings -- 3.7. Immersions |
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3.8. Convenient Submanifolds -- 3.9. Convenient Bundles -- 3.10. Convenient Vector Bundles -- 3.11. Convenient Tangent Bundles -- 3.12. Convenient Vector Fields -- 3.13. Convenient Cotangent Bundles -- 3.14. Convenient Differential Forms -- 3.15. Connections on a Convenient Bundle -- 3.16. Convenient Lie Groups and Lie Algebras -- 3.17. Convenient Principal Bundles -- 3.18. Convenient Lie Algebroids -- 3.19. Classical Results on Banach Structures Which Are Not True in the Convenient Setting -- 3.20. Notes -- 4. Projective Limits -- 4.1. Projective Limits in Categories |
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4.2. Projective Limits of Topological Spaces -- 4.3. Projective Limits of Banach and Normed Spaces -- 4.4. Projective Limits and Linear Functionals -- 4.5. Projective Limits of Differential Maps -- 4.6. Projective Limits of Banach Manifolds -- 4.7. Projective Limits of Banach-Lie Groups -- 4.8. Projective Limits of Banach and Normed Vector Bundles -- 4.9. The Infinite Jet Bundle -- 4.10. Projective Limits of Banach Principal Bundles -- 4.11. The Fréchet Space H(F1, F2) and the Banach Space Hb (F1, F2) -- 4.12. Projective Limits of Generalized Frame Bundles |
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4.13. Projective Limits of G-Structures -- 4.14. Projective Limits of Tensor Structures -- 4.15. Darboux Charts on a Projective Limit -- 4.16. Examples and Counter Example -- 4.17. Projective Limits of Finsler-Banach Manifolds -- 4.18. Projective Limits of Anchored Bundles and Lie Algebroids -- 4.19. Notes -- 5. Direct Limits -- 5.1. Direct Limits of Categories -- 5.2. Direct Limits of Topological Spaces -- 5.3. Ascending Sequences of Normed Spaces -- 5.4. Ascending Sequences of Banach Spaces -- 5.5. Differential Equations on Direct Limits of Banach Spaces |
| Summary |
This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures |
| Notes |
Description based upon print version of record |
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5.6. Direct Limits of Ascending Sequences of Banach Manifolds |
| Form |
Electronic book
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| Author |
Pelletier, Fernand
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| ISBN |
9781000966015 |
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1000966011 |
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