Abstract
In this chapter, we show that a tvs that is a Baire space and admits a countably compact resolution is metrizable, separable and complete. We prove that a linear map T:E→F from an F-space E having a resolution {K α :α∈ℕℕ} into a tvs F is continuous if each restriction T|K α is continuous. This theorem (due to Drewnowski) was motivated by the Arias–De Reina–Valdivia–Saxon theorem about non-Baire dense hyperplanes in Banach spaces. We provide a large class of weakly analytic metrizable and separable Baire tvs that are not analytic (clearly such spaces are necessarily not locally convex).
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© 2011 Springer Science+Business Media, LLC
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Kąkol, J., Kubiś, W., López-Pellicer, M. (2011). K-analytic Baire Spaces. In: Descriptive Topology in Selected Topics of Functional Analysis. Developments in Mathematics, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0529-0_7
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DOI: https://doi.org/10.1007/978-1-4614-0529-0_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-0528-3
Online ISBN: 978-1-4614-0529-0
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