We can denote the lattice operations on as , , , , . By and we denote the minimal and maximal elements of this poset. So set-theoretically, is the filter generated by the union , is the intersection , and similarly for and , while is the improper filter (the power set) and is the filter generated by the empty set, which is .
Revised on September 13, 2013 19:50:33
by Toby Bartels