Some properties of complete congruence lattices (Q1966160)

For a lattice \(L\), denote by \(\text{JCon}(L)\) the lattice of all join complete congruences on \(L\). Of course, Con\((L)\) is always a complete meet-subsemilattice of \(\text{JCon}(L)\). The main results: Theorem 4.3. If \(C\) is a continuous complete lattice then Con\((C)\) is a complete sublattice of \(\text{JCon}(C)\). Corollary 5.4. If \(C\) is continuous then Con\((C)\) is pseudocomplemented.