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) .
Next, for each layer λ and ε > 0, write
Xελ =
{x∈X :
f(Vε(x)) =
Vελ(x)
}
.
[ >> ]