| Title:
|
Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces (English) |
| Author:
|
Margalef-Roig, J. |
| Author:
|
Outerelo-Domínguez, E. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
145-164 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove the existence of a closed neat embedding of a Hausdorff paracompact Hilbert manifold with smooth boundary into $H \times [0, + \infty)$, where $H$ is a Hilbert space, such that the normal space in each point of a certain neighbourhood of the boundary is contained in $H \times \{ 0 \}$. Then, we give a neccesary and sufficient condition that a Hausdorff paracompact topological space could admit a differentiable structure of class $\infty$ with smooth boundary. (English) |
| Keyword:
|
neat embedding |
| Keyword:
|
Hilbert manifold |
| Keyword:
|
manifold with smooth boundary |
| Keyword:
|
normal bundle manifold |
| Keyword:
|
collar neighbourhood |
| MSC:
|
57R40 |
| MSC:
|
58B10 |
| MSC:
|
58C25 |
| idZBL:
|
Zbl 0849.57026 |
| idMR:
|
MR1308351 |
| . |
| Date available:
|
2008-06-06T21:26:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107504 |
| . |
| Reference:
|
[1] R. Abraham: Lectures of Smale Differential Topology.Columbia University, New York, 1962. |
| Reference:
|
[2] S. Armas-Gómez J. Margalef-Roig E. Outerelo-Domínguez E. Padrón-Fernández: Embedding of an Urysohn differentiable manifold with corners in a real Banach space.Winter School of Geometry and Physics held in SRNI (January, 1991, Czechoslovak). |
| Reference:
|
[3] H. Cartan: Sur les Rétractions d’une varieté.C.R. Acad. Sc. Paris, A. 303, Serie I, n. 14, 1986, p. 715. Zbl 0609.32021, MR 0870703 |
| Reference:
|
[4] J. Eells K.D. Elworthy: Open embeddings of certain Banach manifolds.Ann. of Math. 91, 1970, 465–485. MR 0263120 |
| Reference:
|
[5] R. Godement: Théorie des faisceaux.Hermann, Paris, 1958. Zbl 0080.16201, MR 0102797 |
| Reference:
|
[6] J. Margalef-Roig E. Outerelo-Domínguez: Topología diferencial.C.S.I.C., Madrid, 1988. MR 0939168 |
| Reference:
|
[7] J. Margalef-Roig E. Outerelo-Domínguez: On Retraction of Manifolds with corners.(to appear). MR 1303795 |
| Reference:
|
[8] J.H. McAlpin: Infinite dimensional manifolds and Morse theory.Ph.D. Thesis, Columbia University, New York, 1965. |
| Reference:
|
[9] R.E. Stong: Notes on Cobordism Theory.Princeton University Press, 1968. Zbl 0181.26604, MR 0248858 |
| . |
