Grauert's approximation theorem
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In mathematics, Grauert's approximation theorem, due to Grauert, is an analog of Whitney’s approximation theorem for real-analytic maps. It states: with respect to the Whitney topology (also known as strong topology), the space of real-analytic maps between real-analytic manifolds is dense in the space of smooth maps between those manifolds.[1] In the compact case, the theorem is due to Morrey.[2] The case when there is an analytic Riemannian metric is due to Bochner.[3]
