Vol. 15, No. 3, 1965

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Maximal convex filters in a locally convex space

Frank J. Wagner

Vol. 15 (1965), No. 3, 1087–1092

Let E[𝒯 ] be a locally convex space, B a saturated covering of E by bounded sets, and Ethe topological dual of E[𝒯 ]. Let 𝒯B be the topology on Eof uniform convergence on sets of B and E′′ the topological dual of Ef[𝒯B]. We assume E′′ has the natural topology 𝒯n—that of uniform convergence on the equicontinuous sets of E.

This article includes the following: (1) an intrinsic characterization for a bounded convex set B of E of the closure B of B in E′′; (2) an intrinsic characterization of the closure E of E in E′′ ; and (3) necessary and sufficient conditions that E be E′′.

Mathematical Subject Classification
Primary: 46.01
Revised: 11 January 1965
Published: 1 September 1965
Frank J. Wagner