On countable unions of nonmeager sets in hereditarily Lindelöf spaces (Q1760248)

Let \(V\subset\mathbb{R}\) be a Vitali set, so that its translates \(V+r\) for \(r\in\mathbb{Q}\) form a disjoint cover of \(\mathbb{R}\). The paper under review proves that whenever \(A\) is a nonempty proper subset of \(\mathbb{Q}\), the union \(\bigcup_{r\in A}(V+r)\) fails to have the Baire property. It also gives a necessary and sufficient condition for the union to have the Vitali property, i.e.\ to contain a set of the form \(O\setminus M\) where \(O\) is nonempty and open and \(M\) is meagre. The results are obtained by establishing theorems concerning the union of countably many nonmeagre subsets of a hereditarily Lindelöf space.