Smooth finite dimensional embeddings

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We give necessary and sufficient conditions for a norm-compact subset of a Hubert space to admit a C1 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 C1 submanifold of the ambient Hubert space. This work sharpens and extends earlier results of G. Glaeser on paratingents. As byproducts we obtain smoothing theorems for compact subsets of Hubert space and disjunction theorems for locally compact subsets of Euclidean space.

Original languageEnglish (US)
Pages (from-to)585-615
Number of pages31
JournalCanadian Journal of Mathematics
Volume51
Issue number3
DOIs
StatePublished - Jun 1999

Fingerprint

Hubert Space
Subset
Euclidean space
n-dimensional
Structure Theorem
Locally Compact
Theorem
Submanifolds
Smoothing
Norm
Necessary Conditions
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Mansfield, R. ; Movahedi-Lankarani, H. ; Wells, R. / Smooth finite dimensional embeddings. In: Canadian Journal of Mathematics. 1999 ; Vol. 51, No. 3. pp. 585-615.
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Smooth finite dimensional embeddings. / Mansfield, R.; Movahedi-Lankarani, H.; Wells, R.

In: Canadian Journal of Mathematics, Vol. 51, No. 3, 06.1999, p. 585-615.

Research output: Contribution to journalArticle

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