# Definition:Convex Set (Order Theory)/Definition 2

## Definition

A subset $A$ of an ordered set $\left({S, \preceq}\right)$ is convex (in $S$) if and only if:

$\forall x, y \in A: \forall z \in S: x \prec z \prec y \implies z \in A$

## Also see

• Results about convex sets can be found here.