Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592861 | Journal of Functional Analysis | 2007 | 43 Pages |
Abstract
Let G be a Lie group which is the union of an ascending sequence G1⊆G2⊆⋯ of Lie groups (all of which may be infinite-dimensional). We study the question when in the category of Lie groups, topological groups, smooth manifolds, respectively, topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C∞-diffeomorphisms of a σ-compact smooth manifold M; and for test function groups of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups.
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