Sentence:  On the <WSD>Cartesian product</WSD> of two manifolds a differentiable structure can be constructed in the following way. 
Meaning of the word marked with <WSD> tags:  The set of points in an (m + n)-dimensional Cartesian space corresponding to all possible pairs of points from the two sets from spaces of dimension m and n. Notation:  X \times Y = \{ (x_1, ... x_m, y_1, ... y_n) \| (x_1, ... x_m)\in X \land (y_1, ... y_n)\in Y \}.