Editing Glossary of order theory (section)

== T ==

* '''Top'''. See ''unit''.
* '''[[Total order]]'''. A total order ''T'' is a partial order in which, for each ''x'' and ''y'' in ''T'', we have ''x'' ≤ ''y'' or ''y'' ≤ ''x''. Total orders are also called ''linear orders'' or ''chains''.
* '''[[Connected relation|Total relation]]'''.  Synonym for ''[[Connected relation]]''.
* '''[[Transitive relation]]'''. A [[Homogeneous relation|relation]] ''R'' on a set ''X'' is transitive, if ''x R y'' and ''y R z'' imply ''x R z'', for all elements ''x'', ''y'', ''z'' in ''X''.
* '''[[Transitive closure]]'''.  The transitive closure R<sup>&lowast;</sup> of a relation R consists of all pairs ''x'',''y'' for which there exists a finite chain ''x'' R ''a'', ''a'' R ''b'', ..., ''z'' R ''y''.<ref name=BosSuz/>