Here are two such basic broken V neighborhoods
of points on each of the two x-axes, with horizontal displacement
strictly less than twice the finger heights of their broken V neighborhoods.
These intersect nontrivially; any other pairs of broken V
neighborhoods of distinct x-axis points will always be disjoint.
Here are two such basic broken V neighborhoods
of points on each of the two x-axes, with horizontal displacement
strictly less than twice the finger heights of their broken V neighborhoods.