Pointwise topology on completely distributive lattices (Q1117488)

In the recent years the fuzzy topology has developed considerably. Since all fuzzy sets on a non-empty set form a lattice, the fuzzy topology is a topology on a lattice. Now the author generalizes the theory of fuzzy topology to a theory of pointwise topology on complete, completely distributive lattices. The main topics are following: (1) reconstructing the neighborhood structure, the Q-neighborhoods of fuzzy points are replaced by so-called remote-neighborhoods of molecules. (2) Zadeh's functions between fuzzy topological spaces are replaced by a lattice-wise mapping (so called generalized order-homomorphism). The paper contains a lot of interesting results. Obviously the theory presented here may be furthermore developed.