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In general topology, the lexicographic ordering on the unit square (sometimes the dictionary order 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 ==
The lexicographical ordering gives a total ordering
≺
{\displaystyle \prec }
on the points in the unit square: if (x,y) and (u,v) are two points in the square, (x,y)
≺
{\displaystyle \scriptstyle \prec }
(u,v) if and only if either x < u or...