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Embedding of Hilbert manifolds with smooth boundary into semispaces of Hilbert spaces. (English) Zbl 0849.57026

For a differentiable Hilbert manifold \(M\) with \(\partial^2M \neq \emptyset\) it is constructed a real Hilbert space \(H\), an open set \(U \subset H \times [0,\infty)\) and a smooth homeomorphism \(h : M \to U\) such that \(h(\partial M) = U \cap (H \times \{0\})\). The authors give also necessary and sufficient conditions under which a topological space \(X\) admits a Hilbert differentiable structure with \(\partial X \neq \emptyset\) and \(\partial^2 X = \emptyset\).
Reviewer: T.Banakh (Lviv)

MSC:

57R40 Embeddings in differential topology
58C25 Differentiable maps on manifolds
58B10 Differentiability questions for infinite-dimensional manifolds
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