topological spaces), the set of all Cartesian products between one basis element from each gives a basis for the product topology of . That is, for a finite product, the set of all , where each is an element of the (chosen) basis of , is a basis for the product topology of .

The product topology on is the topology generated by the sets of the form , where and is an open subset of . A subset of is open if and only if it is the union