2019/07/25 by Fucai Lin, Lin, Fucai, Zhongbao Tang +1
Mathematics · #54A35 #54G20 #54H11 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Rings, Modules, and Algebras #primary 22A05 #secondary 54A25
paper · pdf · doi:10.48550/arxiv.1907.11037
openalex publication_date 2019/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two non-discrete Hausdorff group topologies τ, δ on a group G are called \it transversal if the least upper bound τ\vee δ of τ and δ is the discrete topology. In this paper, we discuss the existence of transversal group topologies on locally pseudocompact, locally precompact or locally compact groups. We prove that each locally pseudocompact, connected topological group satisfies CSP, which gives an affirmative answer to a problem posed by Dikranjan, Tkachenko and Yaschenko in 2006. For a compact normal subgroup K of a locally compact totally disconnected group G, if G admits a transversal group topology then G/K admits a transversal group topology, which give a partial answer again to a problem posed by Dikranjan, Tkachenko and Yaschenko in 2006. Moreover, we characterize some classes of locally compact groups that admit transversal group topologies.