Topological generators for full groups of hyperfinite pmp equivalence relations

Abstract

We give an elementary proof that there are two topological generators for the full group of every aperiodic hyperfinite probability measure preserving Borel equivalence relation. Our proof explicitly constructs topological generators for the orbit equivalence relation of the irrational rotation of the circle, and then appeals to Dye's theorem and a Baire category argument to conclude the general case.