Abstract
This chapter introduces (after Cascales and Orihuela) a large class of locally convex spaces under the name the class \(\mathfrak{G}\). The class \(\mathfrak{G}\) contains among others all (LM)-spaces (hence (LF)-spaces), and dual metric spaces (hence (DF)-spaces), spaces of distributions D′(Ω) and spaces A(Ω) of real analytic functions on open Ω⊂ℝn. We show (following Cascales and Orihuela) that every precompact set in an lcs in the class \(\mathfrak{G}\) is metrizable. This general result covers many already known theorems for (DF)-spaces, (LF)-spaces and dual metric spaces.
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© 2011 Springer Science+Business Media, LLC
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Kąkol, J., Kubiś, W., López-Pellicer, M. (2011). Metrizability of Compact Sets in the Class \(\mathfrak {G}\) . 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_11
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DOI: https://doi.org/10.1007/978-1-4614-0529-0_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-0528-3
Online ISBN: 978-1-4614-0529-0
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