On topological MV-algebras and topological ℓ-groups

We prove a representation theorem for complete MV-algebras endowed with a Hausdorff order continuous (o.c.) locally convex topology which admits a 0-neighbourhood base consisting of sublattices and deduce from this a representation theorem for Hausdorff o.c. locally solid Dedekind complete ℓ-groups which admits a 0-neighbourhood base consisting of sublattices.