Differentiable Closed Embeddings of Banach Manifolds

Nicolaas H. Kuiper and Besseline Terpstra-Keppler

A chapter in Essays on Topology and Related Topics, 1970, pp 118-125 from Springer

Abstract: Abstract In this paper a manifold X is a C k -manifold which is paracompact, normal, separable, and of differentiability class k, modelled on a separable Banach space B, whose norm is a k-times continuously differentiable function outside 0∈B, k≦ ∞. B with that norm is called a C k -Banach space. Mac Alpin [9] and Colojoara [3, 4] proved that every C∞-Hilbert- manifold has a smooth closed split embedding in the Hilbertspace l 2.

Keywords: Banach Space; Separable Banach Space; Banach Manifold; Finite Codimension; Topological Embedding (search for similar items in EconPapers)
Date: 1970
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-49197-9_11

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DOI: 10.1007/978-3-642-49197-9_11

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