In a poset or even proset, the down set of an element is the set
In a quasiorder, the strict down set of is the set
If you think of a poset as a category, then the down set of is the coslice category .
A down set in the opposite of is an up set in .
Note: The term ‘down set’ is also often used for a lower set, a more general concept. In the terminology above, the down set of is the lower set generated by .
Revised on November 14, 2016 18:18:53
by Toby Bartels