A selection theorem for group actions

John Patton Burgess

Vol. 80 (1979), No. 2, 333–336

DOI: 10.2140/pjm.1979.80.333

Abstract

Let a Polish group G act continuously on a Polish space X, inducing an equivalence relation E. Let E_Y be the restriction of E to an invariant Borel subset Y of X. Assume E_Y is countably separated. Then it has a Borel transversal.

Mathematical Subject Classification 2000

Primary: 54H15

Secondary: 03E15, 46L05, 04A15

Milestones

Received: 21 July 1978

Published: 1 February 1979