  We show that $C(X)$ admits an equivalent pointwise lower semicontinuous
locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral
height 3. In other words $X$ admits a fully closed map $f$ onto a metric
compact $Y$ such that $f^{-1}(y)$ is metrizable for all $y\in Y$ . A continuous
map of compacts $f : X \to Y$ is said to be fully closed if for any disjoint
closed subsets $A;B \subset X$ the intersection $f(A) \cap f(B)$ is finite. For
instance the projection of the lexicographic square onto the first factor is
fully closed and all its fibers are homeomorphic to the closed interval.
