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The (strong) Whitney embedding theorem states that every smooth manifold (Hausdorff and sigma-compact) of dimension has an embedding of smooth manifolds in the Euclidean space of dimension .
Notice that it is easy to see that every smooth manifold embeds into the Euclidean space of some dimension (this prop.). The force of Whitney’s strong embedding theorem is to find the lowest dimension that still works in general.
Named after Hassler Whitney.
See also
Wikipedia, Whitney embedding theorem
Paul Rapoport, Introduction to Immersion, Embeddingand the Whitney Embedding Theorem, 2015 (pdf)
Last revised on December 15, 2020 at 15:04:21. See the history of this page for a list of all contributions to it.