On embeddings of compact manifolds

[fresh_42]

I have found the following entry on his blog by Terence Tao about embeddings of compact manifolds into Euclidean space (Whitney, Nash). It contains the theorems and (sketches of) proofs. Since it is rather short some of you might be interested in.

 

[JorisL]

hehe, I used that post a couple of days ago when I was checking an argument I was trying to use :)
Very useful indeed.

 

[lavinia]

A triangulated manifold with n vertexes naturally embeds in the standard n- simplex in $R^n$. But this embedding is high dimensional and not smooth.