Note that the basic broken neighborhoods V_ε⁰(x) and V_ε'¹(y) of points on the x-axes of different layers will be disjoint — unless 0 < |x-y| < 2·min{ε, ε'}, in which case they will meet at exactly one point, lying over ((x+y)/2, |x-y|/2) .

  Any other pairs of broken V neighborhoods of distinct x-axis points, on whichever layers, will always be disjoint.

  In particular, for fixed layer λ, V_ε^λ(x) ∩ V_ε^λ(y) = ∅ unless x = y .

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