Hamel-isomorphic images of the unit ball

✍ Scribed by Jacek Cichoń; Przemysław Szczepaniak

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 119 KB
• Volume: 56
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200910113

✦ Synopsis

Abstract

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ^2^ and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non‐measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non‐measurable (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)