Now, given a section f for the projection p
from this double-cover to Heath’s
V-space,
consider the set
X = {x∈R : f is
continuous in a neighborhood of
(x, 0)}.
For such x, by continuity, there are layer λ and
real ε > 0 such that
f carries Vε(x)
homeomorphically onto Vελ(x) (the full basic broken V of height ε
centered at f(x, 0) = (x, 0, λ)) .
F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus