Silverman, Stephen Intervals contained in arithmetic combinations of sets. (English) Zbl 0838.28002 Am. Math. Mon. 102, No. 4, 351-353 (1995). In this paper, the author gets the following result, which is a further extension of a classical one by Steinhaus: Theorem. Let \(G\) and \(H\) be dense \(G_\delta\) sets in non-empty open intervals \(I\) and \(J\), respectively. If \(\&\) is any one of the four arithmetic operations \(+\), \(-\) \(\cdot\) or \(/\), then \[ G\& H= I\& J, \] except that in the case of multiplication and division 0 might be in \(I\& J\) but not in \(G\& H\). Reviewer: B.Le Gac (Marseille) Cited in 5 Documents MSC: 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets 54E52 Baire category, Baire spaces Keywords:measure zero sets; second category set; Steinhaus theorems; dense \(G_ \delta\) sets; arithmetic operations PDFBibTeX XMLCite \textit{S. Silverman}, Am. Math. Mon. 102, No. 4, 351--353 (1995; Zbl 0838.28002) Full Text: DOI