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A talk exploring spaces of continuous functions on limits of inverse systems of compact spaces with fully closed bonding mappings, presented at the Workshop on "Structures in Banach Spaces" at the Erwin Schrödinger International Institute for Mathematics and Physics. Discover how these systems can be characterized through the relationship between continuous functions on the limit and continuous functions on certain types of trees. Learn about fully closed mappings between Hausdorff compacta, where the intersection of images of any two closed disjoint subsets is finite. Explore Fedorchuk compact spaces, which occur when the fibers of neighboring bonding mappings are metrizable, and understand how these properties enable locally uniformly rotund renormings on spaces of continuous functions for a specific subclass of Fedorchuk compacta.
