The convenient setting for real analytic mappings

@article{Kriegl1990TheCS,
  title={The convenient setting for real analytic mappings},
  author={Andreas Kriegl and Peter W. Michor},
  journal={Acta Mathematica},
  year={1990},
  volume={165},
  pages={105-159}
}
We present here "the" cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completeness conditions the second requirement can be replaced by: real analytic along ane lines. Enclosed and necessary is a careful study of locally convex topologies on spaces of real analytic mappings. As… 
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