For P a partially ordered set, let S be a subset of P such that if:


a,c\in S and b\in P and a<=b<=c then b\in S


Is there a name for a subset with this property? The term "dense" subset is already taken and means something else.



name for "solid" subset of a partially ordered set?
A set with this property is called *convex*.


See e.g. Quasi-uniform spaces, Volume 77 of Lecture notes in pure and applied mathematics, Peter Fletcher, William F. Lindgren, Marcel Dekker, 1982, p.84.


