Let E[𝒯 ] be a locally convex
space, B a saturated covering of E by bounded sets, and E′ the topological dual of
E[𝒯 ]. Let 𝒯B be the topology on E′ of 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′′.
