Borel transversals and ergodic measures on indecomposable continua

Abstract

AbstractThe first three parts of a theorem of Effros have been crucial to recent investigations in continua theory. The purpose of this paper is to examine some other parts of this theorem and apply them to continua theory as well.Here is one such application. A Borel transversal to the composants of an indecomposable continuum X is a Borel subset B of X such that B intersects each composant of X in exactly one point. It has been unknown for any indecomposable continuum whether or not it has a Borel transversal to its composants. In this paper it is shown that solenoids and Knaster continua do not have Borel transversals to their composants