Real Analytic Curves in Fréchet Spaces and Their Duals.
Reflexivity of inductive limits
An inductive locally convex limit of reflexive topological spaces is reflexive iff it is almost regular.
Regular inductive limits of K-spaces.
A well-known result for bounded sets in inductive limits of locally convex spaces is the following: If each of the constituent spaces En are Fréchet spaces and E is the inductive limit of the spaces En, then each bounded subset of E is bounded in some En iff E is locally complete. Using DeWilde's localization theorem, we show here that the completeness of each En and the local completeness of E may be replaced with the conditions that the spaces En are all webbed K-spaces and E is locally Baire,...
Regularity, barrelledness and dual strong unions in locally convex spaces.
Regularity of conservative inductive limits.
Regularity of general weighted inductive limits.
Remarks on bounded sets in -spaces
We establish the relationship between regularity of a Hausdorff -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff -space to be an -space. A factorization theorem for -spaces with property (K) is also obtained.