Аннотация:Every homogeneous topological space X is naturally associated with
its group of homeomorphisms Hom (X) which transitively acts
on X. A topology on a group Hom (X) (a subgroup of Hom (X)) is called admissible if the group in this topology is a topological group and its action is continuous. Admissible
topologies on the groups of homeomorphisms (subgroups which actions
are transitive) allow us to study both homogeneous spaces using the
theory of topological groups and topological groups as
transformation groups of correspondent homogeneous spaces.
Approaches how to find groups which transitively act on homogenous
spaces and their admissible topologies will be considered in the
talk.