Thin and thick sets in locally convex spaces (Q885315)

The author departs from the concepts of \([w^\ast]\)-thick and \([w^\ast]\)-thin sets that are used to prove, e.g., boundedness and surjectivity theorems in normed and Banach spaces. The author's idea is to generalize these concepts to locally convex spaces. Since only norms have bounded neighborhoods at 0, one can however hardly say that Definition 3 generalizes \(w^\ast\)-thick sets, as the author puts it in his Remark 4. \(w^\ast\)-thickness is designed to conclude that a set in a normed space \(X\) is uniformly norm-bounded as soon as it is pointwise bounded on the \(w^\ast\)-thick set \(A\) in the dual. Thickness, as defined in the paper under review is, as the author demonstrates, closely linked to equicontinuity and barrelledness.