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In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if, intuitively, any point in X can be "well-approximated" by points in A. Formally, A is dense in X if for any point x in X, any neighborhood of x contains at least a point from A. Equivalently, A is dense in X if the only closed subset of X containing A is X itself. This can also be expressed by saying that the closure of A is X, or that the interior of the complement of A is empty. An alternative definition in the case of metric spaces is the following: The set A in a metric space X is dense if every in is a limit of a sequence of elements in A.
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