 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/e/e3/a/i/solution

A

is the intersection of every closed subset containing it:

\overline{A} = ⋂ {F \subseteq X : F closed and A \subseteq F} .

The collection is nonempty because it contains

X

. Arbitrary intersections of closed sets are closed, so this is the smallest closed set containing

A

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