We investigate conditions on a computable metric space under which each co-computably enumerable set satisfying certain topological properties must be computable. We examine the notion of local computability and show that the result by which in a computable metric space which has the effective covering property and compact closed balls each co-c.e. circularly chainable continuum which is not chainable must be computable can be generalized to computable metric spaces which have the effective covering property and which are locally compact. We also give examples which show that neither of these two assumptions can be omitted.
展开▼
