Differential geometry MOC Whitney embedding theorem The Whitney embedding theorem establishes the equivalence of πΆβ differentiable manifolds and real submanifolds, as well as placing an upper bound on the Euclidean dimension required to embed a given manifold. Let π be an π-dimensional πΆβ differentiable manifold. Then π is diffeomorphic to a real embedded manifold of β2π, i.e. π may be smoothly embedded in β2π. diff Proof proof develop | en | SemBr