Hilbert manifold

Manifold modelled on Hilbert spaces

In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dimensional setting. Analogous to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable.

This keyword could refer to multiple things. Here are some suggestions: