Subset of Convex Set can be Uniquely Expressed as Partition of Maximal Convex Sets

Theorem

Let $\struct {S, \preccurlyeq}$ be an ordered set.

Then $S$ can be uniquely expressed as the partition whose components are maximally convex sets.

Proof

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Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $39$. Order Topology: $2$