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Smooth Finite Dimensional Embeddings
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- Journal:
- Canadian Journal of Mathematics / Volume 51 / Issue 3 / 01 June 1999
- Published online by Cambridge University Press:
- 20 November 2018, pp. 585-615
- Print publication:
- 01 June 1999
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- Article
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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 
$\text{G}$. 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.
