The open sets in the product topology are unions (finite or infinite) of sets of the form formula_14 where each formula_15 is open in formula_3 and formula_17 for only finitely many formula_18 In particular, for a finite product (in particular, for the product of two topological spaces), the set of all Cartesian products between one basis element from each formula_3 gives a basis for the product topology of formula_20 That is, for a finite product, the set of all formula_14 where formula_15 is an element of the (chosen) basis of formula_5 is a basis for the product topology of formula_20