Topological lattice ordered groups

Several types of hulls and completions of lattice ordered groups have been obtained by algebraic methods. In this paper is laid some groundwork for the application of topolo-gical and uniform-space concepts to the same end by setting forth those links—topological, algebraic and semantic— between a topological lattice ordered group H and a topologically dense /-subgroup G. In section one a convex /-subgroug of a representable /-group G is proved to be order closed if and only if it is closed with respect to every Hausdorff /-topology. In section three the disjunc-tive formulas which hold in a topological /-group are proved to be the same as those which hold in a topologically dense /-subgroup. The last section contains the continuous versions of the classical /-group representation theorems. The list of contributors to the theory of topological lattic