Barrelled Countable Enlargements and the Dominating Cardinal

✍ Scribed by S.A. Saxon; L.M. Sánchez Ruiz

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 157 KB
• Volume: 203
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0405

✦ Synopsis

Extensively treated by Robertson, Tweddle, Yeomans, Perez Carerras, and Bonet in the 1980s, the barrelled countable enlargement problem may be stated as follows: Let E be a barrelled locally convex space with EЈ / E*. Is there an / -dimensional subspace M of E* transverse to EЈ such that E endowed with the 0 Ž . Mackey topology E, EЈ q M is also barrelled? While the general problem remains open, for E metrizable we give here a complete positive solution under the Ž . assumption that scales exist an assumption weaker than Martin's Axiom .