| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4660881 | Topology and its Applications | 2008 | 8 Pages |
Abstract
We show the limits of Mackey's theorem applied to identity sets to prove that a given group has a unique Polish group topology.Verbal sets in Abelian Polish groups and full verbal sets in the infinite symmetric group are Borel. However this is not true in general.A Polish group with a neighborhood π-base at 1 of sets from the σ-algebra of identity and verbal sets has a unique Polish group topology. It follows that compact, connected, simple Lie groups, as well as finitely generated profinite groups, have a unique Polish group topology.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
