Lattices of closure operators (Q1377730)

The system of all closure operators on a set \(V\) forms in a natural way a lattice which is isomorphic to the lattice of all Moore families \((\text{MF}(V),\subseteq)\) of subsets of \(V\). The author shows the existence of a spanning tree for the lattice of Moore families. Hence all Moore families and all closure operators (of a set \(V\)) can be found using the depth-first search algorithm. For \(| V|= 3\) the diagram \(\text{MF}(V)\) and the corresponding spanning tree are given.