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A class of closed, bounded, convex sets in the Banach space is shown to be a complete PCA set.
Three sets occurring in functional analysis are shown to be of class PCA (also called ) and to be exactly of that class. The definition of each set is close to the usual objects of modern analysis, but some subtlety causes the sets to have a greater complexity than expected. Recent work in a similar direction is in [1, 2, 10, 11, 12].
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