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.
@article{107504,
author = {J. Margalef-Roig and Enrique Outerelo-Dom\'\i nguez},
title = {Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces},
journal = {Archivum Mathematicum},
volume = {030},
year = {1994},
pages = {145-164},
zbl = {0849.57026},
mrnumber = {1308351},
language = {en},
url = {http://dml.mathdoc.fr/item/107504}
}
Margalef-Roig, J.; Outerelo-Domínguez, Enrique. Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces. Archivum Mathematicum, Tome 030 (1994) pp. 145-164. http://gdmltest.u-ga.fr/item/107504/
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