Definition:Order Isomorphism

Definition
Let $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ be ordered sets.

Well-Ordered Sets
When $\struct {S, \preceq_1}$ and $\struct {T, \preceq_2}$ are well-ordered sets, the condition on the order preservation can be relaxed:

Also see

 * Equivalence of Definitions of Order Isomorphism
 * Definition:Relation Isomorphism, from which it can be seen that order isomorphism is a special case.
 * Inverse of Increasing Bijection need not be Increasing


 * Definition:Order Embedding