What's the name of this property?

Question

Is there a name for (partially or totally) ordered set $(A,<)$ such that for any $x,y\in A$, $x< y$ there is a $z\in A$ such that $x<z<y$?

Answer 1

http://en.wikipedia.org/wiki/Dense_order

From Wikipedia : "In mathematics, a partial order < on a set X is said to be dense if, for all x and y in X for which x < y, there is a z in X such that x < z < y."

Answer 2

This would be that no chain has a maximal element, the opposite conclusion of Zorn's Lemma.