Vol. 63, No. 2, 1976

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Generalized inductive limit topologies and barrelledness properties

Wolfgang Ruess

Vol. 63 (1976), No. 2, 499–516

For a locally convex space (X,τ) and an increasing sequence (Aν)νN of convex, circled subsets of X the generalized inductive limit topology related to (X,τ) and (Aν)νN is defined to be the finest locally convex topology on X agreeing with τ on the sets Aν, 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
Received: 27 March 1975
Revised: 8 December 1975
Published: 1 April 1976
Wolfgang Ruess