Geodesic
On various types of barrelledness and the hereditary property of (DF)-spaces
Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 134-143

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

Recently, Levin and Saxon [5], De Wilde and Houet [2] defined the σ-barrelledness while Husain [3] defined the countable barrelledness and countable quasibarrelledness. It is well-known that barrelled spaces are countably barrelled, and countably barrelled spaces are σ-barrelled. It is natural to ask whether there is some condition for σ-barrelled (resp. countably barrelled) spaces to be countably barrelled (resp. barrelled). Using the concept of S-absorbent sequences of sets, we are able to give such conditions in Theorem 2.5 and Corollaries 2.6 and 2.7. 
Husain, T.; Wong, Yau-Chuen. On various types of barrelledness and the hereditary property of (DF)-spaces. Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 134-143. doi: 10.1017/S001708950000286X
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