aDepartment of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706-1388, USA
bDepartment of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3
Abstract:
For a Polish group let be the minimal number of translates of a fixed closed nowhere dense subset of required to cover . For many locally compact this cardinal is known to be consistently larger than which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups . For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach space with an unconditional basis and the group of homeomorphisms of various compact spaces.