We develop differentiation theory based on a new definition of derivative: in terms of integrals of curves. It applies to a very wide class of domains. Some 'elementary' maps between Fréchet spaces, excluded from calculus by previous theories, now emerge as smooth maps.

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Persistent URL dx.doi.org/10.1007/BF01302783
Journal Monatshefte für Mathematik
Nel, L. (1990). Infinite dimensional calculus allowing nonconvex domains with empty interior. Monatshefte für Mathematik, 110(2), 145–166. doi:10.1007/BF01302783