  Locally solid Riesz spaces have been widely investigated in the past several
decades; but locally solid topological lattice-ordered groups seem to be
largely unexplored. The paper is an attempt to initiate a relatively systematic
study of locally solid topological lattice-ordered groups. We give both
Robert-Namioka-type characterization and Fremlin-type characterization of
locally solid topological lattice-ordered groups. In particular, we show that a
group topology on a lattice-ordered group is locally solid if and only if it is
generated by a family of translation-invariant lattice pseudometrics. We also
investigate (1) the basic properties of lattice group homomorphism on locally
solid topological lattice-ordered groups; (2) the relationship between
order-bounded subsets and topologically bounded subsets in locally solid
topological lattice-ordered groups; (3) the Hausdorff completion of locally
solid topological lattice-ordered groups.
