M-SCOTT CONVERGENCE AND M-SCOTT TOPOLOGY ON POSETS

For a subset system M on any poset, M-Scott notions, such as M-way below relation, M-continuity, M-Scott convergence (of nets and filters respectively) and M-Scott topology are proposed. Any approximating auxiliary relation on a poset can be represented by an M-way below relation such that this poset is M-continuous. It is shown that a poset isM-continuous iff the M-Scott topology is completely distributive. The topology induced by the M-Scott convergence coincides with the M-Scott topology. If the M-way below relation satis es the property of interpolation, then a poset is M-continuous if and only if the M-Scott convergence coincides with the M-Scott topological convergence. Also, M-continuity is characterized by a certain Galois connection.