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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 tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embedding
MSC Classifications: 57R99, 58A20 show english descriptions None of the above, but in this section
Jets
57R99 - None of the above, but in this section
58A20 - Jets
 

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