Abstract
Last winter I attended a lecture by A.W. Hager on the countable
lifing property. Suppose one has a ring homomorphism T from
C(X) onto C(Y),
where X and Y are Tychonoff. The question was whether the
following is true: does a countable pairwise othogonal set of
functions bn
in C(Y) lift to a family of pairwise orthogonal functions
an in C(X) so that
T(an) = bn for each n.
A counterexample was sought after, but it turns
out that the result holds.