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 two broken-V nbhds   Note that the basic broken neighborhoods Vε0(x) and Vε'1(y) of points on the x-axes of different layers will be disjoint — unless
0 < ½|x−y| < min{ε, ε'},
in which case they will meet at exactly one point, lying over (½(x+y), ½|x−y|) .

  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, Vελ(x) ∩ Vελ(y) = ∅ unless x = y .