Past exam of the options II course of the University of Oxford / 2012 / E / E3 / a / i

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- Solution i

Solution

The closure of

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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