Smooth Finite Dimensional Embeddings

Mansfield, R. ; Movahedi-Lankarani, H. ; Wells, R.

Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 585-615

Résumé

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.

Détail

DOI : 10.4153/CJM-1999-027-1

Mots-clés : 57R99, 58A20, tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embedding

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