Muthuvel, Kandasamy Application of covering sets. (English) Zbl 0931.26002 Colloq. Math. 80, No. 1, 115-122 (1999). \(A\subset {\mathbb R}\) is called \(\kappa\)-covering set if for each \(X\subset {\mathbb R}\), \(|X|\leq\kappa\), there is a \(t\in{\mathbb R}\) such that \(X+t\subset A\). The author proves several theorems about covering sets which generalize and unify some results about the additive subgroups of the reals and the algebraic difference of sets (see B. King [Real Anal. Exch. 19, No. 2, 478-490 (1994; Zbl 0804.28002)] and K. Muthuvel [Real Anal. Exch. 20, 819-822 (1995; Zbl 0828.26002)]). He shows in particular that the complement of a finite union of proper subgroups of \({\mathbb R}\) is of the size continuum and nowhere meager. Reviewer: T.Natkaniec (Gdańsk)) Cited in 1 ReviewCited in 3 Documents MSC: 26A03 Foundations: limits and generalizations, elementary topology of the line 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 03E15 Descriptive set theory Keywords:Hamel basis; Erdős set; covering set Citations:Zbl 0804.28002; Zbl 0828.26002 PDFBibTeX XMLCite \textit{K. Muthuvel}, Colloq. Math. 80, No. 1, 115--122 (1999; Zbl 0931.26002) Full Text: DOI EuDML