The Convenient Setting of Global Analysis

@inproceedings{Kriegl1997TheCS,
  title={The Convenient Setting of Global Analysis},
  author={Andreas Kriegl and Peter W. Michor},
  year={1997}
}
Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications References Index. 
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We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued
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Synthetic Geometry of Manifolds
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Implicit Functions from Topological Vector Spaces to Banach Spaces
. We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not
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Let M be a separable C∞ Finsler manifold of infinite dimension. Then it is proved, amongst other results, that under suitable conditions of local extensibility the germ of a C∞ function, or of a C∞
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