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 X with an atlas of coordinate charts over Fréchet spaces whose transitions are smooth mappings. Thus X has an open cover {U_α}_{α ε I}, and a collection of homeomorphisms φ_α : U_α → F_α onto their images, where F_α are Fréchet spaces, such that

is smooth for all pairs of indices α, β.

[edit] References

1. Hamilton, R. S., The inverse function theorem of Nash and Moser, Bull AMS 7 (1982) no. 1, 65-222.