Fréchet manifold
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In mathematics, in particular in nonlinear analysis, a Fréchet manifold is a topological space modeled on a Fréchet space in much the same way as a manifold is modeled on a Euclidean space.
More precisely, a Fréchet manifold consists of a Hausdorff space with an atlas of coordinate charts over Fréchet spaces whose transitions are smooth mappings. Thus
has an open cover
and a collection of homeomorphisms
onto their images, where
are Fréchet spaces, such that
is smooth for all pairs of indices