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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 26th 2024
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: ## Statement Every real-analytic $n$-dimensional second countable Hausdorff manifold admits a real-analytic, regular and proper embedding into a euclidean space $\mathbf{R}^k$ of sufficiently high dimension. ## Related concepts * [[Whitney embedding theorem]] * [[Narasimhan embedding theorem]] * [[Nash embedding theorem]] ## References The original reference is Theorem 3 in * [[Hans Grauert]], _On Levi's Problem and the Imbedding of Real-Analytic Manifolds_, Annals of Mathematics, Second Series, Vol. 68, No. 2 (Sep., 1958), pp. 460-472, [doi](https://doi.org/10.2307/1970257). <a href="https://ncatlab.org/nlab/revision/Grauert+embedding+theorem/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Grauert+embedding+theorem">current</a>

   Created:

   Statement

   Every real-analytic $n$-dimensional second countable Hausdorff manifold admits a real-analytic, regular and proper embedding into a euclidean space $\mathbf{R}^k$ of sufficiently high dimension.

   Related concepts

   • Whitney embedding theorem

   • Narasimhan embedding theorem

   • Nash embedding theorem

   References

   The original reference is Theorem 3 in

   • Hans Grauert, On Levi’s Problem and the Imbedding of Real-Analytic Manifolds, Annals of Mathematics, Second Series, Vol. 68, No. 2 (Sep., 1958), pp. 460-472, doi.

   v1, current