Editing Glossary of order theory (section)

== R ==

* '''Reflecting'''. A function ''f'' between posets ''P'' and ''Q'' is said to reflect suprema (joins), if, for all subsets ''X'' of ''P'' for which the supremum sup{''f''(''x''): ''x'' in ''X''} exists and is of the form ''f''(''s'') for some ''s'' in ''P'', then we find that sup ''X'' exists and that sup ''X'' = ''s'' . Analogously, one says that ''f'' reflects finite, non-empty, directed, or arbitrary joins (or meets). The converse property is called ''join-preserving''.
* '''[[Reflexive relation|Reflexive]]'''. A [[binary relation]] ''R'' on a set ''X'' is reflexive, if ''x R x'' holds for every element ''x'' in ''X''.
* '''Residual'''.  A dual map attached to a [[residuated mapping]].
* '''[[Residuated mapping]]'''.  A monotone map for which the preimage of a principal down-set is again principal.  Equivalently, one component of a Galois connection.