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1 results

  • Appendix A - A Primer on Topological Vector Spaces and Locally Convex Spaces

  • Alexander Schmeding, Nord Universitet, Norway
  • Book:
    An Introduction to Infinite-Dimensional Differential Geometry
    Published online:
    08 December 2022
    Print publication:
    22 December 2022, pp 186-205
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  • 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