L O ] 2 4 A ug 2 01 8 TOPOLOGICALLY 2-GENERATED GROUPS

We formulate and prove general conditions implying that the automorphism group Aut(M) of a countable structure M , and the group L0(Aut(M)) of measurable functions with values in Aut(M), have a cyclically dense conjugacy class, in particular, are topologically 2-generated. This provides a number of new examples of groups with this property.