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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. — 1993

Proceedings of the Winter School "Geometry and Physics"

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...

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

J. Margalef-Roig;  Enrique Outerelo-Domínguez — 1994

Archivum Mathematicum

In this paper we prove the existence of a closed neat embedding of a Hausdorff paracompact Hilbert manifold with smooth boundary into H × [ 0 , + ∞ ) , 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 × { 0 } . Then, we give a neccesary and sufficient condition that a Hausdorff paracompact topological space could admit a differentiable structure of class ∞ with smooth boundary.

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