Here's a fairly easy fact from point-set topology that I'm having trouble finding a reference for. Say $X$ is a total order satisfying the least-upper bound property, and $S$ is a closed subset of it. Then the subspace topology on $S$ and the order topology on $S$ coincide.

Does anyone know what would be a reference I can cite for this fact so I don't have to take up space in my paper to include a proof?

Actually, I'm pretty certain I've seen a proof of this statement given either here or else on math.stackexchange, but I haven't been able to find it. Those aren't ideal references, obviously, but still seem preferable to taking up space including a proof myself...

Thank you all!