Closure of a Set

For any set A in a topological space X, the closure of A is the intersection of all closed subsets containing A.
Intuitively, this is the small closed set that contains A.
That is, \bar{A} = \bigcup_{B \subset A, B \in \mathcal{C}} where \mathcal{C} is the set of all closed sets in X.
Some properties:
* Avery set is by definition contained in its closure: A \subseteq \bar{A}
* A set A is closed if and only if A = \bar{A}
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