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. Equivalently, every nonempty open subset of X intersects A.

• 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.