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Smooth extensions and spaces of smooth and holomorphic mappings. (English) Zbl 1108.58006
This note presents a possible definition of smooth (resp. complex) manifolds with corners modeled on locally convex spaces. The definition extends naturally the finite-dimensional case. Being given a compact (resp. complex) manifold \(M\) with corners and a smooth (resp. complex) Lie group \(K\), the space of smooth (resp. holomorphic) mappings from \(M\) to \(K\) is then shown to be a smooth (resp. complex) Lie group. The proof is largely based on former work by H. Gl√∂ckner [J. Funct. Anal. 194, No. 2, 347–409 (2002; Zbl 1022.22021)].

MSC:
58B25 Group structures and generalizations on infinite-dimensional manifolds
58A05 Differentiable manifolds, foundations
46A03 General theory of locally convex spaces
46T10 Manifolds of mappings
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