Now, given a section f for the projection p from this double-cover to Heath’s V-space, consider the set X = {x∈R : f is continuous in a neighborhood of (x, 0)}.   For such x, by continuity, there are layer λ and real ε > 0 such that f carries V_ε(x) homeomorphically onto V_ε^λ(x) (the full basic broken V of height ε centered at f(x, 0) = (x, 0, λ)) .       [ >> ]