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A topological space X is a Volterra space if the intersection of any two dense Gδ-sets of X is dense in X. Clearly every Baire space is Volterra and there exists an example of a non-Baire space which is first countable, completely regular and paracompact [G. F. Gruenhage and D. J. Lutzer, Proc. Amer. Math. Soc. 128 (2000), no. 10, 3115–3124; MR1664398 (2000m:54030)]. The authors obtain several special cases for which every Volterra space is Baire, thus answering in the positive some naturally posed questions, e.g. for stratifiable spaces and for locally convex spaces. The paper also provides examples of non-Baire spaces, such as X(σ(X, X ′)) if X ′ contains an infinite linearly independent pointwise bounded subset. This result is well known in the particular case that X is an infinite-dimensional normed space as a consequence of the Hahn-Banach Theorem

Year: 2013

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