Geodesic
On the Stability of Barrelled Topologies II
Glasgow mathematical journal, Tome 21 (1980) no. 1, pp. 91-95

Voir la notice de l'article provenant de la source Cambridge University Press

If E is a Hausdorff barrelled space, which does not already have its finest locally convex topology, then the continuous dual E′ may be enlarged within the algebraic dual E*. Robertson and Yeomans [10] have recently investigated whether E can retain the barrelled property under such enlargements. Whereas finite-dimensional enlargements of the dual preserve barrelledness, they have shown that this is not always so for countable-dimensional enlargements E′+M. In fact, if E contains an infinitedimensional bounded set, there always exists a countable-dimensional M for which the Mackey topology τ(E, E′+M) is not barrelled [10, Theorem 2]. 
Tweddle, I.; Yeomans, F. E. On the Stability of Barrelled Topologies II. Glasgow mathematical journal, Tome 21 (1980) no. 1, pp. 91-95. doi: 10.1017/S0017089500004043
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[1] 1.Bourbaki, N., Espaces vectorieh topologiques, Chap. III–V (Paris, 1967). Google Scholar

[2] 2.de Wilde, M., Closed graph theorems and webbed spaces (London, 1978). Google Scholar

[3] 3.de Wilde, M. and Houet, C., On increasing sequences of absolutely convex sets in locally convex spaces, Math. Ann. 192 (1971), 257–261. Google Scholar | DOI

[4] 4.Dieudonné, J., Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Polon. Math. 25 (1952), 50–55. Google Scholar

[5] 5.Drake, F. R., Set theory (Amsterdam, 1974). Google Scholar

[6] 6.Grothendieck, A., Topological vector spaces (London, 1973). Google Scholar

[7] 7.Mackey, G. W., On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155–207. Google Scholar | DOI

[8] 8.Nachbin, L., Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 471–474. Google Scholar PubMed | DOI

[9] 9.Robertson, A. P. and Robertson, W. J., Topological vector spaces, 2nd edition (Cambridge, 1973). Google Scholar

[10] 10.Robertson, W. J. and Yeomans, F. E., On the stability of barrelled topologies I, Bull. Austral. Math. Soc., to appear. Google Scholar

[11] 11.Shirota, T., On locally convex vector spaces of continuous functions, Proc. Japan Acad. 30 (1954), 294–298. Google Scholar

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