## PCA sets and convexity

### Volume 163 / 2000

Fundamenta Mathematicae 163 (2000), 267-275
DOI: 10.4064/fm-163-3-267-275

#### Abstract

Three sets occurring in functional analysis are shown to be of class PCA (also called $Σ^1_2$) 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].