Non-amenable groups with amenable action and some paradoxical decompositions in the plane
Non-archimedean (uniformly) continuous measures on homogeneous spaces
Non-locally compact Polish groups and two-sided translates of open sets
This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of in terms of group actions, and prove that certain natural classes of non-locally...