We replace measure with category in an argument of GW Mackey to characterize closed
subgroups H of a totally nonmeager, 2nd countable topological group G in terms of the …

We consider the topological Vaught conjecture: If a Polish group $ G $ acts continuously on
a Polish space $ S $, then $ S $ has either countably many or perfectly many orbits. We …

It has been shown by J. Feldman, P. Hahn and CC Moore that every non-singular action of a
second countable locally compact group has a countable (in fact so-called lacunary) …

It is shown that if a second countable locally compact group G acts nonsingularly on an
analytic measure space (S, μ), then there is a Borel subset E⊂ S such that EG is conull in S …

We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic
to a continuous action of the group on a Polish space, and we apply this result to three …

Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility,
and measures preserving group actions considered up to orbit equivalence. This title …

For a continuous action of a countable discrete group G on a Polish space X, a countable
Borel partition P of X is called a generator if GP:={g P: g∈ G, P∈ P} generates the Borel σ …

We prove that if (G,·) is a group with a metric, separable, and Baire topology T such that h→
g· h is continuous for all gϵG and g→ g· h is Baire measurable for all hϵG, then (G, T) is a …

We present a simple approach to questions of topological orbit equivalence for actions of
countable groups. For example, for any action of a countable group ΓΓ on a topological …

The study of continuous group actions is ubiquitous in mathematics, and perhaps the most
general kinds of actions for which we can hope to prove theorems in just ZFC are those …