Stone topology of the set of prime filters of a 0-distributive lattice (Q1431055)

Let \(L\) be a distributive lattice and let \(P(L)\) denotes the set of all prime filters of \(L\). Considers sets \(r(a)= \{F\in P(L): a\in L\}\). Then we can introduce a topology on \(P(L)\) defining sets \(r(a)\) to be a subbase of the open sets. This topology is called the Stone topology on \(P(L)\). Now, the author studies the Stone topology for bounded \(0\)-distributive (1-distributive) lattices. (A \(0\)-distributive lattice is a lattice satisfying the following condition: \(a\wedge b= 0= a\wedge c\) implies \(a\wedge(b\vee c)= 0\).) The author obtains some necessary and sufficient conditions for the subspace of maximal filters to be normal.