Dense

The term dense has at least two different meanings in mathematics.

• A subset A of a topological space X is said to be dense 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. Equivalently, every nonempty open subset of X intersects A. As an example, the set of rational numbers is a dense subset of the real numbers.

• A partial order on a set S is said to be dense if, for all x and y in S for which x < y, there is a z in S such that x < z < y. The rational numbers with the ordinary ordering are a densely ordered set in this sense.

See also density in physics.