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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Canadian Journal of Mathematics
( Vol. 51 NO.3 / (1999))
Smooth Finite Dimensional Embeddings
R. Mansfield, H. Movahedi-Lankarani, R. Wells,
Pages. 585-615
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.
Contents 1. Introduction
2. The tangent space and quasibundles
3. The stopping theorem
4. Projection on the tangent space
5. The projection theorem
6. An alternative form of the embedding theorem
7. Smoothing and disjunction
8. Remarks and examples
Key words tangent space, diffeomorphism, manifold, spherically compact, paratingent, quasibundle, embedding
Mathmatical Subject Classification 57R99, 58A20