Editing Glossary of order theory (section)

== O ==

* '''Order-dual'''.  The order dual of a partially ordered set is the same set with the partial order relation replaced by its converse.
* '''[[Order-embedding]]'''. A function ''f'' between posets ''P'' and ''Q'' is an order-embedding if, for all elements ''x'', ''y'' of ''P'', ''x'' ≤ ''y'' (in ''P'') is equivalent to ''f''(''x'') ≤ ''f''(''y'') (in ''Q'').
* '''[[Order isomorphism]]'''. A mapping ''f'': ''P'' → ''Q'' between two posets ''P'' and ''Q'' is called an order isomorphism, if it is [[bijective]] and both ''f'' and ''f''<sup>−1</sup> are [[monotone function]]s. Equivalently, an order isomorphism is a surjective ''order embedding''.
* '''[[Order-preserving]]'''. See ''monotone''.
* '''[[Order-reversing]]'''. See ''antitone''.