2011/01/24 by Montserrat Bruguera, Bruguera, Montserrat, Mikhail Tkachenko +1
Mathematics · #22D35 #54C10 #54E52 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.GN #math.GR #msc:22C05 #msc:22D35 #msc:43A40 #msc:54C10 #msc:54E52 #primary 43A40 #secondary 22C05
paper · pdf · doi:10.48550/arxiv.1101.4504
arxiv created 2011/01/24 · openalex publication_date 2011/01/24 · arxiv updated 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a wide class of reflexive, precompact, non-compact, Abelian topological groups G determined by three requirements. They must have the Baire property, satisfy the open refinement condition, and contain no infinite compact subsets. This combination of properties guarantees that all compact subsets of the dual group G^\wedge are finite. We also show that many (non-reflexive) precompact Abelian groups are quotients of reflexive precompact Abelian groups. This includes all precompact almost metrizable groups with the Baire property and their products. Finally, given a compact Abelian group G of weight ≥ 2^\om, we find proper dense subgroups H1 and H2 of G such that H1 is reflexive and pseudocompact, while H2 is non-reflexive and almost metrizable.