Extreme set

Summary

An extreme set of a set $A$ is a subset $B$ of $A$ with the following property. Whenever a point of $B$ lies strictly between two points of $A$, both of those points lie in $B$. It generalises the notion of extreme point: a point is extreme exactly when the one-point set it forms is an extreme set. The convex extreme subsets of a convex set are its faces.