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

Margalef-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 -