ABSTRACT

Recursive sets in the Euclidean space are those sets which can be effectively approximated by finitely many points for an arbitrary given precision. On the other hand, co-recursively enumerable sets are those sets whose complements can be effectively covered by open balls. If a set is recursive, then it is co-recursively enumerable, however the converse is not true in general. In this paper we investigate the subsets of the Euclidean space called triods and we prove that each co-r.e. triod with computable endpoints is recursive.