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# Smooth Finite Dimensional Embeddings

Published:1999-06-01
Printed: Jun 1999
• R. Mansfield
• H. Movahedi-Lankarani
• R. Wells
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## Abstract

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
 MSC Classifications: 57R99 - None of the above, but in this section 58A20 - Jets

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