 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2007/e/e2/solution

T_{A} = {A \cap U : U \in T} .

These sets contain the empty set and

A

, are closed under arbitrary unions, and are closed under finite intersections because intersections distribute over the common factor

A

. Thus they form a topology on

A

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