Differential geometry MOC

Whitney embedding theorem

The Whitney embedding theorem establishes the equivalence of differentiable manifolds and real submanifolds, as well as placing an upper bound on the Euclidean dimension required to embed a given manifold. Let be an -dimensional differentiable manifold. Then is diffeomorphic to a real embedded manifold of , i.e. may be smoothly embedded in . #m/thm/geo/diff

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