NMSU • BLAST-2009
Something Old, Something New, Something Borrowed, ...
F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus
Note that the basic broken neighborhoods
V
ε
0
(
x
)
and
V
ε'
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,
V
ε
λ
(
x
) ∩
V
ε
λ
(
y
) = ∅
unless
x
=
y
.