Generalized inductive limit topologies and barrelledness properties

Wolfgang Ruess

Vol. 63 (1976), No. 2, 499–516

DOI: 10.2140/pjm.1976.63.499

Abstract

For a locally convex space (X,τ) and an increasing sequence (A_ν)_ν∈N of convex, circled subsets of X the generalized inductive limit topology related to (X,τ) and (A_ν)_ν∈N is defined to be the finest locally convex topology on X agreeing with τ on the sets A_ν, ν ∈ N. Several results on the classification and the inheritance properties of various types of barrelledness and their evaluable analogs are shown to be consequences only of a few basic properties of such an inductive limit topology and, in this way, are deduced and extended in a unified manner.

Mathematical Subject Classification

Primary: 46A07, 46A07

Milestones

Received: 27 March 1975

Revised: 8 December 1975

Published: 1 April 1976