  We give an example of a compact metric space $K$, an open dense subset $U$ of
$K$, and a sequence $(f_n)$ in $C(K)$ which is pointwise convergent to a
non-continuous function on $K$, such that for every $u \in U$ there exists $n
\in \N$ with $f_n(u)=f_m(u)$ for all $m \geq n$, yet $(f_n)$ is equivalent to
the unit vector basis of the James quasi-reflexive space of order 1. Thus $c_0$
does not embed isomorphically in the closed linear span $[f_n]$ of $(f_n)$.
This answers in negative a question asked by H. Haydon, E. Odell and H.
Rosenthal.
