This is a Munkres's problem: Let Y be an ordered set with the ordered topology and f,g functions from X to Y, show that the set$\displaystyle \{x:f(x)\leq g(x)\}$ is closed. I can show this, for intance, when Y=R(real numbers set) but I can't prove this if Y is just an ordered set because it may have consecutive elements. Any comments will be appreciated