Two counterexamples to Cornea's conjecture on thin sets
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.
scientific article; zbMATH DE number 755439