 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/e/e4/a/i/solution

U \subseteq X / R open ⟺ p^{- 1} (U) open in X .

Preimages commute with arbitrary unions and finite intersections and take the empty and whole sets to the corresponding sets, so this definition indeed gives a topology.

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