Embedding of a Urysohn differentiable manifold with corners in a real Banach space

Armas-Gómez, S. ; Margalef-Roig, J. ; Outerolo-Domínguez, E. ; Padrón-Fernández, E.

Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1993), p. [143]-152 / Harvested from

Résumé

Summary: We prove a characterization of the immersions in the context of infinite dimensional manifolds with corners, we prove that a Hausdorff paracompact $C^{p}$ -manifold whose charts are modelled over real Banach spaces which fulfil the Urysohn $C^{p}$ -condition can be embedded in a real Banach space, $E$ , by means of a closed embedding, $f$ , such that, locally, its image is a totally neat submanifold of a quadrant of a closed vector subspace of $E$ and finally we prove that a Hausdorff paracompact topological space, $X$ , is a Hilbert $C^{\infty}$ -manifold without boundary if and only if $X$ is homeomorphic to $A$ , where $A$ is a $C^{\infty}$ -retract of an open set of a real Hilbert space.

MR MR1246628 | Zbl 0871.57018

EUDML-ID : urn:eudml:doc:221142
Mots clés:

@article{701513,
     title = {Embedding of a Urysohn differentiable manifold with corners in a real Banach space},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1993},
     pages = {[143]-152},
     mrnumber = {MR1246628},
     zbl = {0871.57018},
     url = {http://dml.mathdoc.fr/item/701513}
}

Armas-Gómez, S.; Margalef-Roig, J.; Outerolo-Domínguez, E.; Padrón-Fernández, E. Embedding of a Urysohn differentiable manifold with corners in a real Banach space, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1993), pp. [143]-152. http://gdmltest.u-ga.fr/item/701513/