High Quality Content by WIKIPEDIA articles! In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below). Banach manifolds are one possibility of extending manifolds to infinite dimensions. A further generalisation is to Frechet manifolds, replacing Banach spaces by Frechet spaces. On the other hand, a Hilbert manifold is a special case of a Banach manifold in which the manifold is locally modelled on Hilbert spaces.

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