A Generalization of the Lowen Functor ωL

This paper generalize the Lowen functor based on a complete lattice with an approximating relation (with the property of interpolation). It is shown that, on any completely distributive lattice, the Lowen functor ω L can not only defined by \(\nleq\) relation, but also by the way below relation < < and the wedge below relation \(\vartriangleleft\).