A topology on lattice-ordered groups

Abstract

We introduce the concept of the strong-positive cone in a lattice-ordered group (G,6, ·) and define the continuous latticeordered group. We also investigate the C-topology and bi-C-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) (G,6, ·) is a continuous lattice-ordered group if and only if (G,6) is a continuous poset; (2) for the bi-C-topology τ in a continuous lattice-ordered group (G,6, ·), (G, ·, τ) is a topological group and (G,6, τ) is a topological lattice.