An Isomorphism Theorem for Partial Numberings

As is well-known, two equivalent total numberings are computably isomorphic, if at least one of them is precomplete. Selivanov asked whether a result of this type is true also for partial numberings. As has been shown by the author, numberings of this kind appear by necessity in studies of effectively given topological spaces like the computable real numbers. In the present paper it is demonstrated for a rather general class of spaces including the computable reals that any two strongly correct numberings are computably isomorphic. Moreover, two strongly equivalent partial numberings are computably isomorphic, if they are both correctly precomplete, or uniformly productive.