In general topology, the lexicographic ordering on the unit square is a topology on the unit square S, i.e. on the set of points (x,y) in the plane such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. == Construction == As the name suggests, we use the lexicographical ordering on the square to define a topology. Given two points in the square, say (x,y) and (u,v), we say that (x,y) (u,v) if and only if either x < u or both x = u and y < v. Given the lexicographical ordering on the square, we use the order topology to define the topology on S. == Properties == The order topology makes S into a completely normal...