Two counterexamples to Cornea's conjecture on thin sets
type: Item
instance of: scholarly article
title: Two counterexamples to Cornea's conjecture on thin sets
zbMATH Open document ID: 0838.31009
author: Pavel Pyrih
published in: Osaka Journal of Mathematics
publication date: 1995-05-15T00:00:00Z
review text: A conjecture of A. Cornea states that a set \(A \subset \mathbb{R}^n\) is thin at 0, i.e. 0 is not a limit point of \(A\) w.r.t. the fine topology, if there exist \(v_1, v_2, v_3 \in \mathbb{R}^n\) linearly independent (pairwise, if \(n = 2)\), \(|v_j |= 1\), such that \(T_{v_j} (A)\) is thin at 0, \(j = 1,2,3\), where \(T_v (x) = x - \langle x,v \rangle \cdot v\). The author gives counterexamples in dimension 2 and 3 using the Wiener criterion for thinness.
Mathematics Subject Classification ID: 31C40
zbMATH DE Number: 755439
zbMATH Keywords: thin set
zbMATH Keywords: counterexamples
zbMATH Keywords: Wiener criterion
reviewed by: Walter Hoh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 755439