The Countable Lifting Property for C(X)

**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 *b _{n}*
in