PCA sets and convexity
Copyright policy )PCA sets and convexity
Summary: Three sets occurring in functional analysis are shown to be of class PCA (also called \(\Sigma_2^1)\) 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.
norm, Isomorphic theory (including renorming) of Banach spaces, Banach space, convex sets, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Convex sets in topological linear spaces; Choquet theory, integrals over extreme points, analytic set, co-analytic set, Borel set, PCA set, Descriptive set theory
norm, Isomorphic theory (including renorming) of Banach spaces, Banach space, convex sets, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Convex sets in topological linear spaces; Choquet theory, integrals over extreme points, analytic set, co-analytic set, Borel set, PCA set, Descriptive set theory
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