Dense

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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.

See also density in physics.