We prove a full completeness theorem for MLL without the Mix rule. This is done by interpreting a proof as a dinatural transformation in a *-autonomous category of reflexive topological abelian groups first studied by Barr, denoted [Rscr][Tscr][Ascr]. In Section 2, we prove the unique interpretation theorem for a binary provable MLL-sequent. In Section 3, we prove a completeness theorem for binary sequents in MLL without the Mix rule, where we interpret formulas in the category [Rscr][Tscr][Ascr]. The theorem is proved by investigating the concrete structure of [Rscr][Tscr][Ascr], especially that arising from Pontrjagin's work on duality.