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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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