I generalized a theorem in the preprint article “Filters on posets and generalizations” on my Algebraic General Topology site.
The new theorem is formulated as following:
Theorem If is a join-closed filtrator and is a meet-semilattice and is a complete lattice, then
From this theorem also follow the following formulas about funcoids:
The problem, whether meet of any two discrete funcoids is the same on the lattice of all funcoids and on the lattice of discrete funcoids, remains empty.