Abstract
Extensively treated by Robertson, Tweddle, Yeomans, Pérez Carerras, and Bonet in the 1980s, the barrelled countable enlargement problem may be stated as follows: LetEbe a barrelled locally convex space withE′≠E*. Is there an ℵ0-dimensional subspaceMofE* transverse toE′ such thatEendowed with the Mackey topology μ(E,E′+M) is also barrelled? While the general problem remains open, forEmetrizable we give here a complete positive solution under the assumption that scales exist (an assumption weaker than Martin's Axiom).
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