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• W2040207127 abstract "Abstract We prove the following theorems: (1) If X has strong measure zero and if Y has strong first category, then their algebraic sum has property S 0 . (2) If X has Hurewicz's covering property, then it has strong measure zero if, and only if, its algebraic sum with any first category set is a first category set. (3) If X has strong measure zero and Hurewicz's covering property then its algebraic sum with any set in is a set in . ( is included in the class of sets always of first category, and includes the class of strong first category sets.) These results extend: Fremlin and Miller's theorem that strong measure zero sets having Hurewicz's property have Rothberger's property, Galvin and Miller's theorem that the algebraic sum of a set with the γ-property and of a first category set is a first category set, and Bartoszyfński and Judah's characterization of -sets. They also characterize the property (*) introduced by Gerlits and Nagy in terms of older concepts." @default.
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• W2040207127 date "1998-03-01" @default.
• W2040207127 modified "2023-09-30" @default.
• W2040207127 title "The algebraic sum of sets of real numbers with strong measure zero sets" @default.
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• W2040207127 doi "https://doi.org/10.2307/2586602" @default.
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