Quotients of Frechet manifolds

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In finite dimensions there is the quotient manifold theorem. Is there a generalization to infinite dimensions? Does anybody know references or maybe standard references for such questions?

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You can read about Frechet manifolds in "Some recent work in Fréchet geometry" by C. T. J. Dodson and references therein. It is stated on page 8 that:

Hausdorfness implies that a compact subset of a Fréchet space is closed; a closed subspace is a Fréchet space and a quotient by a closed subspace is a Fréchet space.

You can find the same statement on page 4 of part I of "Kähler Geometry of Loop Spaces" by Armen Sergeev (it is free).