2022/09/20 by Yingying Jin, Jin, Ying-Ying, Lihong Xie +1 · 2 citations
Mathematics · #20N05 #22A22 #22A30 #54H11 #54H99 #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2210.03648
openalex publication_date 2022/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A topological gyrogroup is a gyrogroup endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous. In this paper, we study the quotient gyrogroups in topological gyrogroups with respect to strongly L-subgyrogroups, and prove that let (G, τ,⊕) be a topological gyrogroup and H a closed strongly L-subgyrogroup of G, then the natural homomorphism π from a topological gyrogroup G to its quotient topology on G/H is an open and continuous mapping, and G/H is a homogeneous T1-space. We also establish that for a locally compact strongly L-subgyrogroup H of a topological gyrogroup G, the natural quotient mapping π of G onto the quotient space G/H is a locally perfect mapping. This leads us to some interesting results on how properties of G depend on the properties of G/H. Some classical results in topological groups are generalized.