Group topologies on automorphism groups of homogeneous structures

TL;DR

This paper classifies all coarser group topologies than stabilizer topologies for automorphism groups of certain homogeneous structures, including the Urysohn space and sphere, advancing understanding of their topological properties.

Contribution

It provides a comprehensive classification of coarser topologies on automorphism groups of specific homogeneous structures, a novel result in the field.

Findings

Classified all coarser topologies than stabilizer topologies for automorphism groups

Extended the classification to the Urysohn space and sphere

Enhanced understanding of the topological structure of automorphism groups

Abstract

We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.