Lattice operators and topologies.
Lattice separation, coseparation and regular measures.
Lattice uniformities on orthomodular structures
Logics with separating sets of measures
Lower semicontinuous functions with values in a continuous lattice
It is proved that for every continuous lattice there is a unique semiuniform structure generating both the order and the Lawson topology. The way below relation can be characterized with this uniform structure. These results are used to extend many of the analytical properties of real-valued l.s.cḟunctions to l.s.cḟunctions with values in a continuous lattice. The results of this paper have some applications in potential theory.