English

An embedding theorem for uniform measures on topological groups

Group Theory 2023-06-06 v4 General Topology

Abstract

The embedding theorem of Roelcke and Dierolf for the completions of four standard uniform structures on topological groups and their quotients holds more generally for spaces of uniform measures. The natural mappings between the four spaces of uniform measures on a topological group are injective and their restrictions to positive cones are topological embeddings. The same holds for spaces of uniform measures on the quotient of a topological group by a neutral subgroup.

Keywords

Cite

@article{arxiv.2207.01956,
  title  = {An embedding theorem for uniform measures on topological groups},
  author = {Jan Pachl},
  journal= {arXiv preprint arXiv:2207.01956},
  year   = {2023}
}

Comments

12 pages; V2 and V3: corrected typos; V4: new section 6

R2 v1 2026-06-24T12:14:20.148Z