smoothly homotopic

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Cohomotopy group — In mathematics, particularly algebraic topology, cohomotopy sets are particular contravariant functors from the category of pointed topological spaces and point preserving continuous maps to the category of sets and functions. They are dual to… … Wikipedia
Hilbert manifold — 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… … Wikipedia

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