Representation theorem of fuzzy lattices and its applications in fuzzy topology (Q1095165)

A completely distributive, complete lattice with an order-reversing map is called fuzzy lattice. Using the notion of ``pole element'', the author gives an expression of a fuzzy lattice in terms of the direct product of minimal fuzzy sublattices. Based on the result, the author establishes also a pointwise characterization of fuzzy complete regularity which was obtained by the reviewer for the case that the fuzzy lattice is \(L^ X\) where L is a fuzzy lattice [Sci. Sin. Ser. A 26, 138-147 (1983; Zbl 0518.54008)].