The intermediate value theorem generalizes in a natural way: Suppose that "X" is a connected topological space and ("Y", <) is a totally ordered set equipped with the order topology, and let "f" : "X" → "Y" be a continuous map. If "a" and "b" are two points in "X" and "u" is a point in "Y" lying between "f"("a") and "f"("b") with respect to <, then there exists "c" in "X" such that "f"("c") = "u". The original theorem is recovered by noting that ℝ is connected and that its natural topology is the order topology.