Computability of 1-manifolds

A semi-computable set S in a computable metric space need not be computable.However, in some cases, if S has certain topological properties, we canconclude that S is computable. It is known that if a semi-computable set S is acompact manifold with boundary, then the computability of \deltaS implies thecomputability of S. In this paper we examine the case when S is a 1-manifoldwith boundary, not necessarily compact. We show that a similar result holds inthis case under assumption that S has finitely many components