Abstract
Comparing the different notions of hypercomplete, B-complete, B r -complete, and complete 1.c. spaces E dealt with in the preceding chapters, one observes that each of these notions depends upon the coincidence of the ew*-topology with the a(E′, E)-topology on some prescribed sets of the dual E′ of E. More precisely, let Q be an arbitrary set of the dual E′ of an 1.c. space E and suppose the following statement is true:
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(A′)
Q is σ(E′, E)-closed if and only if it is ew*-closed.
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© 1965 Springer Fachmedien Wiesbaden
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Husain, T. (1965). Locally Convex Spaces with the B(φ)-Property. In: The Open Mapping and Closed Graph Theorems in Topological Vector Spaces. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96210-2_7
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DOI: https://doi.org/10.1007/978-3-322-96210-2_7
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-322-96077-1
Online ISBN: 978-3-322-96210-2
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