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1. CJM 1999 (vol 51 pp. 585)

Mansfield, R.; Movahedi-Lankarani, H.; Wells, R.
Smooth Finite Dimensional Embeddings
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.

Keywords:tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embedding
Categories:57R99, 58A20

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