Geodesic
Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces
Archivum mathematicum, Tome 30 (1994) no. 3, pp. 145-164.

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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.
Classification : 57R40, 58B10, 58C25
Keywords: neat embedding; Hilbert manifold; manifold with smooth boundary; normal bundle manifold; collar neighbourhood 
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     author = {Margalef-Roig, J. and Outerelo-Dom{\'\i}nguez, E.},
     title = {Embedding of {Hilbert} manifolds with smooth boundary into semispaces of {Hilbert} spaces},
     journal = {Archivum mathematicum},
     pages = {145--164},
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     volume = {30},
     number = {3},
     year = {1994},
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     zbl = {0849.57026},
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     url = {http://geodesic.mathdoc.fr/item/ARM_1994__30_3_a0/}
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Margalef-Roig, J.; Outerelo-Domínguez, E. Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces. Archivum mathematicum, Tome 30 (1994) no. 3, pp. 145-164. http://geodesic.mathdoc.fr/item/ARM_1994__30_3_a0/