Whitney embedding theorem

The Whitney embedding theorem establishes the equivalence of $𝐶 \infty$ differentiable manifolds and real submanifolds, as well as placing an upper bound on the Euclidean dimension required to embed a given manifold. Let $𝑀$ be an $𝑚$ -dimensional $𝐶 \infty$ differentiable manifold. Then $𝑀$ is diffeomorphic to a real embedded manifold of $ℝ 2 𝑚$ , i.e. $𝑀$ may be smoothly embedded in $ℝ 2 𝑚$ . #m/thm/geo/diff

Proof

#missing/proof

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