Abstract
This chapter deals with the class of angelic spaces, introduced by Fremlin, for which several variants of compactness coincide. A remarkable paper of Orihuela introduces a large class of topological spaces X (under the name web-compact) for which the space C p (X) is angelic. Orihuela’s theorem covers many already known partial results providing Eberlein–Šmulian-type results. Following Orihuela, we show that C p (X) is angelic if X is web-compact. This yields, in particular, Talagrand’s result stating that for a compact space X the space C p (X) is K-analytic if and only if C(X) is weakly K-analytic. We present some quantitative versions of Grothendieck’s characterization of the weak compactness for spaces C(X) (for compact Hausdorff spaces X) and quantitative versions of the classical Eberlein–Grothendieck and Krein–Šmulian theorems.
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© 2011 Springer Science+Business Media, LLC
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Kąkol, J., Kubiś, W., López-Pellicer, M. (2011). Web-Compact Spaces and Angelic Theorems. 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_4
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DOI: https://doi.org/10.1007/978-1-4614-0529-0_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-0528-3
Online ISBN: 978-1-4614-0529-0
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