Completeness of locally k_ω-groups and related infinite-dimensional Lie groups

2016/12/29 by Helge Glöckner, Glockner, Helge
Mathematics · #22A05 #22E65 (primary) #46A13 #46M40 #58D05 (secondary) #Advanced Algebra and Geometry #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1612.09111

openalex publication_date 2016/12/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Recall that a topological space is said to be a k_ω-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_ω-space, then X is called locally k_ω. We show that a topological group is complete whenever the underlying topological space is locally k_ω. As a consequence, every infinite-dimensional Lie group modelled on a Silva space is complete.

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