Source: wikibot/lexicographic-order-topology-on-the-unit-square

= Lexicographic order topology on the unit square
{wiki=Lexicographic_order_topology_on_the_unit_square}

The lexicographic order topology on the unit square, which we denote as \\( \[0, 1\] \\times \[0, 1\] \\), is based on an ordering of the points in the unit square. In this topology, we define a way to compare points \\((x_1, y_1)\\) and \\((x_2, y_2)\\) in the square using the lexicographic order, similar to how words are ordered in a dictionary.