 Solution

ID: past-exam-of-the-topology-course-of-the-university-of-oxford/2014/2/a/i/solution

{U \times V : U \subseteq X open, V \subseteq Y open} .

Open subsets of the product are arbitrary unions of these rectangles. The rectangles cover the product and their finite intersections are rectangles, so they satisfy the basis axioms. Equivalently, this is the smallest topology making both coordinate projections continuous.

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