When is a Volterra space Baire? |
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Authors: | Jiling Cao Heikki J.K. Junnila |
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Affiliation: | a School of Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1020, New Zealand b Department of Mathematics and Statistics, The University of Helsinki, PO Box 68, FI-00014, Helsinki, Finland |
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Abstract: | In this paper, we study the problem when a Volterra space is Baire. It is shown that every stratifiable Volterra space is Baire. This answers affirmatively a question of Gruenhage and Lutzer in [G. Gruenhage, D. Lutzer, Baire and Volterra spaces, Proc. Amer. Math. Soc. 128 (2000) 3115-3124]. Further, it is established that a locally convex topological vector space is Volterra if and only if it is Baire; and the weak topology of a topological vector space fails to be Baire if the dual of the space contains an infinite linearly independent pointwise bounded subset. |
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Keywords: | primary, 54E52 secondary, 46A03, 54E20, 54F65, 54H11 |
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