In a poset or even proset, the up set of an element is the set
In a quasiorder, the strict up set of is the set
If you think of a poset as a category, then the up set of is the slice category .
An up set in the opposite of is a down set in .
Note: The term ‘up set’ is also often used for an upper set, a more general concept. In the terminology above, the up set of is the upper set generated by .
Revised on July 1, 2010 17:58:23
by Toby Bartels