Co-c.e. Sets with Disconnected Complements

Abstract

We examine co-c.e. sets with disconnected complements in a computable metric space. We focus on the case when the computable metric space is effectively locally connected and when the connected components of the complement of a co-c.e. set S can be effectively distinguished. We give a sufficient condition that such an S contains a computable point and a sufficient condition that S is computable.