Definition:Convex Set (Order Theory)/Definition 2
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Definition
A subset $A$ of an ordered set $\struct {S, \preceq}$ 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.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $39$. Order Topology: $1$