- 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*, or in other words: the interior of the complement of*A*is empty. 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, as are the real numbers. - A subset
*B*of a partially ordered set*A*is**dense in**if for any*A**x*<*y*in*A*, there is some*z*in*B*such that*x*<*z*<*y*. In case the order is a linear order, then*B*is dense in*A*in the present sense if and only if*B*is dense in the order topology on*A*. Hence the first two meanings above are related.

See also density in physics.