2020/01/02 by Maxime Gheysens, Gheysens, Maxime
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Primary 22F50 #Secondary 54E15 #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2001.00548
openalex publication_date 2020/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the topology of uniform convergence on bounded sets is compatible with the group law of the automorphism group of a large class of spaces that are endowed with both a uniform structure and a bornology, thus yielding numerous examples of topological groups. This encompasses many of previously known cases, such as homeomorphism groups of locally compact spaces, automorphism groups of first-order structures, general linear groups of normed spaces, automorphism groups of uniform spaces, etc. We also study the automorphism group of a topological group within this framework (generalizing previously known results on locally compact groups). As a particular outcome of this machinery, we show that the automorphism group of a Polish locally Roelcke-precompact group carries a natural Polish group topology.