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## Main Question or Discussion Point

Can you define a space that is locally homeomorphic to an infinite dimensional Hilbert space analogously to how you define a (smooth) manifold by an atlas defining local homeomorphisms to R^n?

So the charts would just map to the Hilbert space rather than R^n. Could the rest of the definition be left the same?

So the charts would just map to the Hilbert space rather than R^n. Could the rest of the definition be left the same?