Completeness of locally k-groups and related infinite-dimensional Lie groups
Copyright policy )Completeness of locally k-groups and related infinite-dimensional Lie groups
Recall that a topological space is said to be a $k_��$-space if it is the direct limit of an ascending sequence of compact Hausdorff topological spaces. If each point in a Hausdorff space $X$ has an open neighbourhood which is a $k_��$-space, then $X$ is called locally $k_��$. We show that a topological group is complete whenever the underlying topological space is locally $k_��$. As a consequence, every infinite-dimensional Lie group modelled on a Silva space is complete.
v2: 11 pages, major rewriting, cuts, and change of authorship as the former Theorem 1.1 turned out be a known result by D.C. Hunt and S.A. Morris from 1974
- University of Paderborn Germany
Groups of diffeomorphisms and homeomorphisms as manifolds, Infinite-dimensional Lie groups and their Lie algebras: general properties, hemicompact space, Spaces defined by inductive or projective limits (LB, LF, etc.), Group Theory (math.GR), compactly generated space, 22E65 (primary), 22A05, 46A13, 46M40, 58D05 (secondary), (DFS)-space, Inductive and projective limits in functional analysis, Structure of general topological groups, direct limit, completeness, FOS: Mathematics, Silva space, Mathematics - Group Theory, infinite-dimensional Lie group
Groups of diffeomorphisms and homeomorphisms as manifolds, Infinite-dimensional Lie groups and their Lie algebras: general properties, hemicompact space, Spaces defined by inductive or projective limits (LB, LF, etc.), Group Theory (math.GR), compactly generated space, 22E65 (primary), 22A05, 46A13, 46M40, 58D05 (secondary), (DFS)-space, Inductive and projective limits in functional analysis, Structure of general topological groups, direct limit, completeness, FOS: Mathematics, Silva space, Mathematics - Group Theory, infinite-dimensional Lie group
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