Book contents
- Frontmatter
- Contents
- Preface
- 1 Calculus in Locally Convex Spaces
- 2 Spaces and Manifolds of Smooth Maps
- 3 Lifting Geometry to Mapping Spaces I: Lie Groups
- 4 Lifting Geometry to Mapping Spaces II: (Weak) Riemannian Metrics
- 5 Weak Riemannian Metrics with Applications in Shape Analysis
- 6 Connecting Finite-Dimensional, Infinite-Dimensional and Higher Geometry
- 7 Euler–Arnold Theory: PDEs via Geometry
- 8 The Geometry of Rough Paths
- Appendix A A Primer on Topological Vector Spaces and Locally Convex Spaces
- Appendix B Basic Ideas from Topology
- Appendix C Canonical Manifold of Mappings
- Appendix D Vector Fields and Their Lie Bracket
- Appendix E Differential Forms on Infinite-Dimensional Manifolds
- Appendix F Solutions to Selected Exercises
- References
- Index
Appendix A - A Primer on Topological Vector Spaces and Locally Convex Spaces
Published online by Cambridge University Press: 08 December 2022
Book contents
- Frontmatter
- Contents
- Preface
- 1 Calculus in Locally Convex Spaces
- 2 Spaces and Manifolds of Smooth Maps
- 3 Lifting Geometry to Mapping Spaces I: Lie Groups
- 4 Lifting Geometry to Mapping Spaces II: (Weak) Riemannian Metrics
- 5 Weak Riemannian Metrics with Applications in Shape Analysis
- 6 Connecting Finite-Dimensional, Infinite-Dimensional and Higher Geometry
- 7 Euler–Arnold Theory: PDEs via Geometry
- 8 The Geometry of Rough Paths
- Appendix A A Primer on Topological Vector Spaces and Locally Convex Spaces
- Appendix B Basic Ideas from Topology
- Appendix C Canonical Manifold of Mappings
- Appendix D Vector Fields and Their Lie Bracket
- Appendix E Differential Forms on Infinite-Dimensional Manifolds
- Appendix F Solutions to Selected Exercises
- References
- Index
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
Summary
This section contains some auxiliary results on topological vector spaces and locally convex spaces in particular. Note that for some of the results in this appendix, it is essential that we only consider Hausdorff topological vector spaces (which is the standing assumption in the present book). In some more specialised section, we will discuss the following topics: (1) smooth bump function (or the lack thereof) in locally convex spaces, (2) the (failure of) the inverse function theorem in locally convex spaces, (3) the breakdown of the solution theory to ordinary differential equation, (4) a comparison of Bastiani calculus and the convenient calculus
Keywords
- Type
- Chapter
- Information
- An Introduction to Infinite-Dimensional Differential Geometry , pp. 186 - 205Publisher: Cambridge University PressPrint publication year: 2022
- Creative Commons
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/cclicenses/
You have
Access
Open access