Editing Glossary of order theory (section)

== G ==

* '''[[Galois connection]]'''. Given two posets ''P'' and ''Q'', a pair of monotone functions ''F'':''P'' → ''Q'' and ''G'':''Q'' → ''P'' is called a Galois connection, if ''F''(''x'') ≤ ''y'' is equivalent to ''x'' ≤ ''G''(''y''), for all ''x'' in ''P'' and ''y'' in ''Q''. ''F'' is called the '''lower adjoint''' of ''G'' and ''G'' is called the '''upper adjoint''' of ''F''.
* '''[[Greatest element]]'''. For a subset ''X'' of a poset ''P'', an element ''a'' of ''X'' is called the greatest element of ''X'', if ''x'' ≤ ''a'' for every element ''x'' in ''X''. The dual notion is called ''least element''.
* '''Ground set'''. The ground set of a poset (''X'', ≤) is the set ''X'' on which the partial order ≤ is defined.