1. The problem statement, all variables and given/known data Let X be an ordered set where every closed interval is compact. Prove that X has the least upper bound property. 2. Relevant equations X having the least upper bound property means that every nonempty subset that is bounded from above has a least upper bound, in other words, an upper bound where any number less that it is not an upper bound. Compact means that every open cover has a finite subcover. 3. The attempt at a solution Let A be a subset of X that is bounded from above. I know I should try to find a closed interval from this, but I'm not sure where to get it from.