The 𝑛-separated-arc property for homeomorphisms

Abstract

Abstract.Let/ be a function defined in the open unit disk D whose range is in the Riemann sphere W, and let C denote the unit circle. We show that if / is a homeomorphism of D onto a Jordan domain, then the set of points p&C at which / has the »-separatedarc property («^2) is a subset of the set of ambiguous points of/ and is thus countable.