A Hilbert manifold is a specific type of manifold that is modeled on a Hilbert space, which is a complete inner product space. To understand the concept of a Hilbert manifold, it's helpful to break down the terms involved: 1. **Manifold**: A manifold is a topological space that locally resembles Euclidean space. Formally, it is a topological space where every point has a neighborhood that is homeomorphic to an open subset of Euclidean space.
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