Transversals in Non-Discrete Groups

[摘要] The concept of `topological right transversal' is introduced to study right transversals in topological groups. Given any right quasigroup 𝑆 with a Tychonoff topology 𝑇, it is proved that there exists a Hausdorff topological group in which 𝑆 can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closeed). It is also proved that if a topological right transversal $(S, T_S, T^S, circ)$ is such that $T_S=T^S$ is a locally compact Hausdorff topology on 𝑆, then 𝑆 can be embedded as a right transversal of a closed subgroup in a Hausdorff topological group which is universal in some sense.

[学科分类] 数学（综合）

[关键词] Topological transversal;Hilbert space;free topological group.