Smooth Finite Dimensional Embeddings
Printed: Jun 1999
We give necessary and sufficient conditions for a norm-compact subset
of a Hilbert space to admit a $C^1$ embedding into a finite dimensional
Euclidean space. Using quasibundles, we prove a structure theorem
saying that the stratum of $n$-dimensional points is contained in an
$n$-dimensional $C^1$ submanifold of the ambient Hilbert space. This
work sharpens and extends earlier results of G.~Glaeser on paratingents.
As byproducts we obtain smoothing theorems for compact subsets of
Hilbert space and disjunction theorems for locally compact subsets
of Euclidean space.
tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embedding
57R99 - None of the above, but in this section
58A20 - Jets