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Definition: Let X and Y be topological spaces. The product topology on XxY is the topology having as basis the collection B of all sets of the form UxV, where U is an open subset of X and V is an open subset of U.
Source: Topology (second edition) by James R. Munkres
Example: For a more general case (including technical notation), see http://mathworld.wolfram.com/ProductTopology.html