Definition:Densely Ordered/Subset

Definition
Let $\struct {S, \preceq}$ be an ordered set.

A subset $T \subseteq S$ is said to be densely ordered in $\struct {S, \preceq}$ :
 * $\forall a, b \in S: a \prec b \implies \exists c \in T: a \prec c \prec b$