On porosity and exceptional sets
type: Item
instance of: scholarly article
title: On porosity and exceptional sets
zbMATH Open document ID: 0597.28002
author: Theodore A. Vessey
published in: Real Analysis Exchange
publication date: 1984-01-01T00:00:00Z
review text: Let f be a real valued function defined in the upper half plane \(\{\) (x,y): \(y>0\}\). Let E(f) denote the set of all points x on the real line where f has unequal angular cluster sets on any two Stolz angles with vertexes at the point x. Theorem. If E is a \(G_{\delta \sigma}\), sigma- globally porous set on the real line, then there is a continuous function f from the upper half plane to [0,1], such that \(E=E(f)\). This is a partial answer to a question of \textit{H. Yoshida} [Nagoya Math. J. 46, 111-120 (1972; Zbl 0211.389)]. The paper does not contain the proof of the Theorem. The notion of the sigma-globally porous set was introduced by \textit{P. D. Humke} and the author [Real. Anal. Exch. 8, 262-271 (1983; Zbl 0543.28001)].
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 26B35
Mathematics Subject Classification ID: 30D40
Mathematics Subject Classification ID: 26A15
zbMATH DE Number: 3962038
zbMATH Keywords: exceptional sets
zbMATH Keywords: first Baire category
zbMATH Keywords: angular cluster sets
zbMATH Keywords: Stolz angles
zbMATH Keywords: porous set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3962038