Topology, Cartesian-product spaces

Starting with a pair of topological spaces X1, X2, the Cartesian product of X1 and X2 (written X1 ´ X2) may be constructed as follows: the points of X1 ´ X2 are ordered pairs (a, b) in which a X1 and b X2. Basis elements of X1 ´ X2 are sets of the form U1 ´ U2 in which U1 is a basis element of X1; U2 is a basis element of X2; and U1 ´ U2 denotes the set of all points (x1, x2) of X1 ´ X2 in which x1 U1, x2 U2. In a certain sense, the plane Â2 is the Cartesian product of two lines. Also Âm + n is the Cartesian