Take two copies of the upper half-plane, topologized by ... taking as basic open neighborhoods of points on either x-axis the symmetric “broken open Vs”, with fingers of equal length, but with left finger in the same half-plane as the point on the x-axis, and right finger in the other half-plane (omitting the corresponding point on that other x-axis).

  Depending on the layer λ ∈ {0, 1}, we write V_ε^λ(x) = {(x-r, r, λ) : 0 < r < ε} ∪ {(x+r, r, 1-λ) : 0 < r < ε} (ε > 0, x ∈ R, λ ∈ {0, 1}).

[ >> ]