 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2013/e/1/b/i/solution

{U \times V : U \in T_{X}, V \in T_{Y}} .

X \times Y

, and intersections remain rectangles since

(U_{1} \times V_{1}) \cap (U_{2} \times V_{2}) = (U_{1} \cap U_{2}) \times (V_{1} \cap V_{2})

. One may equivalently take products of elements from a chosen basis of a topology in each factor.

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