New York City Category Theory Seminar
Something Old, Something New, Something Borrowed, ...
Next F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus

double cover with one broken-V nbhd   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 
Vελ(x) = {(x−r, r, λ) : 0 < r < ε} ∪ {(x+r, r, 1−λ) : 0 < r < ε}
(ε > 0, x ∈ R, λ ∈ {0, 1}).