Given a section *f* for the projection *p* from this double-cover
to Heath’s *V*-space, we write *V*_{0} , resp. *V*_{1} ,
for the points (*x*, 0) **on the ***x*-axis of Heath’s *V*-space that
the section *f* carries to the lower, resp. upper, copy in the double cover.

And we write *V*_{0, n} ,
resp. *V*_{1, n} ,
for the set of points (*x*, 0) of *V*_{0} ,
resp. of *V*_{1} ,
for which the section *f* carries the entire basic *V* neighborhood
of (*x*, 0) , of finger-height 1/*n* , to the basic broken *V* neighborhood, of same finger-height, of *f*(*x*, 0) in the double cover.

Anyway, the *x*-axis of Heath’s *V*-space is the join of
*V*_{0} with *V*_{1} .

And, **if ***f* is continuous,
each *V*_{i} is the join of the (nested)
family {*V*_{i, n}}_{n}
(*i* = 0, 1) .

Or, at any rate, the set of *x*-axis points (*x*, 0)
of *V*_{i} at which *f* **is** continuous is just that join.

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