An abelian cancellative semigroup embeds (via a semigroup monomorphism) into an abelian group. What about an abelian cancellative Hausdorff topological semigroup that does *not* embed (via a monomorphism of topological semigroups) into an abelian Hausdorff topological group? And what if the embedding is required to be a homeomorphism when corestricted to the image (endowed with the relative topology induced by the overlying topological group)? 

I'm aware of work of E. Schieferdecker (Math. Ann. **131**, 1956), N. J. Rothman (Math. Ann. **139**, 1960), and a few more authors on the subject, but couldn't find any counterexample in print.