A continuous map from a nonempty compact space to an ordered space attains its minimum and maximum.Suggest a slogan
Let \(f\colon X \to Y\) be continuous, where \(X\) is a nonempty compact space and \(Y\) is an ordered set in the order topology. Then there exist \(c, d\in X\) with \(f(c)\leq f(x)\leq f(d)\) for every \(x\in X\) [@Mun00].