Difference between revisions of "Hard Whitney embedding theorem"

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(New page: {{embedding theorem}} ==Statement== A compact connected differential manifold of dimension <math>n</math> can be embedded inside <math>\R^{2n}</math>. This is an improvement on the Whit...)
 
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Latest revision as of 19:46, 18 May 2008

This article is about an embedding theorem, viz about sufficient conditions for a given manifold (with some additional structure) to be realized as an embedded submanifold of a standard space (real or complex projective or affine space)
View a complete list of embedding theorems

Statement

A compact connected differential manifold of dimension n can be embedded inside \R^{2n}.

This is an improvement on the Whitney embedding theorem, which states that any compact connected differential manifold of dimension n can be embedded inside \R^{2n+1} and immersed inside \R^{2n}.