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 $\struct {S, \preccurlyeq}$.

Also see

• Results about dual orderings can be found here.

Sources

• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations