The topology on the Cartesian product X×Y of two topological spaces whose open sets are the unions of subsets A×B, where A and B are open subsets of X and Y, respectively. This definition extends in a natural way to the Cartesian product of any finite number n of topological spaces. The product topology of R×...×R_︸_(n times), where R is the real line with the Euclidean topology, coincides with the Euclidean topology of the Euclidean space R^n.
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