  If $X$ is compact metrizable and has finite fd-height then the unit interval,
$I$, $\ell$-dominates $X$, in other words, there is a continuous linear map of
$C_p(I)$ onto $C_p(X)$. If the unit interval $\ell$-dominates a space $X$ then
$X$ is compact metrizable and has countable fd-height. Similar results are
given for spaces $\ell$-dominated by the reals.
