Let L be a continuous distributive lower-bounded lattice and l be an element of L . Suppose l L . Then l is prime if and only if there exists an open filter F of L such that l is maximal in - F . Let L be a relational structure and X be a subset of the carrier of L . Let L be a non empty relational structure and p , x be elements of L .
L is Heyting.
Let L be a continuous complete lattice. Let l be an element of L . Let L be a complete lattice. Let L be a complete lattice. Then L is completely-distributive if and only if L is distributive and continuous and L op is continuous.