Definition:Dual of Order Type

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

Let $\varrho = \map \ot {S, \preccurlyeq}$ denote the order type of $\struct {S, \preccurlyeq}$.

The dual of $\varrho$ is defined and denoted as:
 * $\varrho^* = \map \ot {S, \succcurlyeq}$

where $\struct {S, \succcurlyeq}$ is the dual of $\struct {S, \preccurlyeq}$.