抄録
This paper constructs a standard Borel space, PG, and a map p∈PG→G(p) such that each G(p) is a Polish group, and such that every Polish group is isomorphic to at least one of the groups G(p); PG thus serves as a parameter space for all Polish groups. We formulate the notion of a Borel map from a standard B Space to Polish groups, and that of a Borel functor from a standard Borel groupoid to Polish groups; both are defined in terms of the existence of Borel factorizations through PG. We apply these ideas to establish a general “Cohomology Lemma, ” asserting that cocycles, with values in Borel family of Polish groups, may be cobounded into a given family of dense, normal, Borel subgroups, whenever the underlying groupoid is a hyperfmite equivalence relation.
