# Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces

J. Margalef-Roig; Enrique Outerelo-Domínguez

Archivum Mathematicum (1994)

- Volume: 030, Issue: 3, page 145-164
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topMargalef-Roig, J., and Outerelo-Domínguez, Enrique. "Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces." Archivum Mathematicum 030.3 (1994): 145-164. <http://eudml.org/doc/247561>.

@article{Margalef1994,

abstract = {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 \lbrace 0 \rbrace $. 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.},

author = {Margalef-Roig, J., Outerelo-Domínguez, Enrique},

journal = {Archivum Mathematicum},

keywords = {neat embedding; Hilbert manifold; manifold with smooth boundary; normal bundle manifold; collar neighbourhood; embedding; differentiable Hilbert manifold},

language = {eng},

number = {3},

pages = {145-164},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces},

url = {http://eudml.org/doc/247561},

volume = {030},

year = {1994},

}

TY - JOUR

AU - Margalef-Roig, J.

AU - Outerelo-Domínguez, Enrique

TI - Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces

JO - Archivum Mathematicum

PY - 1994

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 030

IS - 3

SP - 145

EP - 164

AB - 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 \lbrace 0 \rbrace $. 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.

LA - eng

KW - neat embedding; Hilbert manifold; manifold with smooth boundary; normal bundle manifold; collar neighbourhood; embedding; differentiable Hilbert manifold

UR - http://eudml.org/doc/247561

ER -

## References

top- R. Abraham, Lectures of Smale Differential Topology, Columbia University, New York, 1962. (1962)
- 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). (1991)
- H. Cartan, Sur les Rétractions d’une varieté, C.R. Acad. Sc. Paris, A. 303, Serie I, n. 14, 1986, p. 715. (1986) Zbl0609.32021MR0870703
- J. Eells K.D. Elworthy, Open embeddings of certain Banach manifolds, Ann. of Math. 91, 1970, 465–485. (1970) MR0263120
- R. Godement, Théorie des faisceaux, Hermann, Paris, 1958. (1958) Zbl0080.16201MR0102797
- J. Margalef-Roig E. Outerelo-Domínguez, Topología diferencial, C.S.I.C., Madrid, 1988. (1988) MR0939168
- J. Margalef-Roig E. Outerelo-Domínguez, On Retraction of Manifolds with corners, (to appear). MR1303795
- J.H. McAlpin, Infinite dimensional manifolds and Morse theory, Ph.D. Thesis, Columbia University, New York, 1965. (1965)
- R.E. Stong, Notes on Cobordism Theory, Princeton University Press, 1968. (1968) Zbl0181.26604MR0248858

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.