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

Locally uniformly rotund renormings of the spaces of continuous functions on Fedorchuk compacts