The starting point for the theory is the fact that every topological space is characterized by a set of points "X" and a system Ω("X") of open sets of elements from "X", i.e. a subset of the powerset of "X". It is known that Ω("X") has certain special properties: it is a complete lattice within which suprema and finite infima are given by set unions and finite set intersections, respectively. Furthermore, it contains both "X" and the empty set. Since the embedding of Ω("X") into the powerset lattice of "X" preserves finite infima and arbitrary suprema, Ω("X") inherits the following distributivity law: