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Smooth Finite Dimensional Embeddings

Published online by Cambridge University Press:  20 November 2018

R. Mansfield ,
H. Movahedi-Lankarani  and
R. Wells
R. Mansfield
Affiliation:
Department of Mathematics, Penn State University, University Park, Pennsylvania 16802, U.S.A. email: melvin@math.psu.edu
H. Movahedi-Lankarani
Affiliation:
Department of Mathematics, Penn State Altoona, Altoona, Pennsylvania 16601-3760, U.S.A. email: hml@math.psu.edu
R. Wells
Affiliation:
Department of Mathematics, Penn State University, University Park, Pennsylvania 16802, U.S.A. email: wells@math.psu.edu
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Abstract

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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.

Keywords

57R9958A20tangent spacediffeomorphismmanifoldspherically compactparatingentquasibundleembedding
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 3 , 01 June 1999 , pp. 585 - 615
Copyright
Copyright © Canadian Mathematical Society 1999

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