Now, given a section f for the projection p from this double-cover to Heath’s V-space, consider the set
X = {xR : 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 Vε(x) homeomorphically onto Vελ(x) .
  Next, for each layer λ and ε > 0, write
Xελ = {xX : f(Vε(x)) = Vελ(x) } . 
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