contradictory requirements on the section   Alas, for any particular i and n, the set Vi, n is at most countable, because distinct points (x, 0) and (y, 0) of one Vi, n must lie at least 2/n apart, as measured by |x – y|. Indeed, whatever the points (x, 0) and (y, 0) of Vi, n , the one thing that is certain about the value |x – y| is that, of the three classically exhaustive possibilities

  |x – y| = 0 ,
0 < |x – y|  < 2/n ,
  |x – y|  > 2/n ,

only the first and third can subsist; for, were the second the case, the section f must send the point at which the two intersecting fingers meet, as the illustrations show, to a point in the double cover that lies at once in both of the broken open Vs shown, which is impossible, as those two broken open Vs are disjoint.

[ >> ]