A topology on lattice-ordered groups
Huanrong Wu, Qingguo Li, Bin Yu · The Journal of Nonlinear Sciences and Applications · 2018
We introduce the concept of the strong-positive cone in a lattice-ordered group \((G,\leq,\cdot)\) and define the continuous lattice-ordered 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) \((G,\leq,\cdot)\) is a continuous lattice-ordered group if and only if \((G,\leq)\) is a continuous poset; (2) for the bi-\(C\)-topology \(\tau\) in a continuous lattice-ordered group \((G,\leq,\cdot)\), \((G,\cdot,\tau)\) is a topological group and \((G,\leq,\tau)\) is a topological lattice.