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Keywords:
$DF$-spaces; countably quasibarrelled spaces
Summary:
Let $(E,t)$ be a Hausdorff locally convex space. Either $(E,\sigma (E,E'))$ or \newline $(E',\sigma (E',E))$ is a $DF$-space iff $E$ is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].
References:
[1] Grothendieck A.: Sur les espaces $(F)$ et $(DF)$. Summa Brasil Math. 3 (1954), 57-123. MR 0075542 | Zbl 0058.09803
[2] Iyahen O., Sunday: Some remarks on countably barrelled and countably quasibarrelled spaces. Proc. Edinburgh Math. Soc. 15 (1966), 295-296. MR 0226357
[3] Radenovič S.: Some remarks on the weak topology of locally convex spaces. Publ. de l'Institut Math. 44 (1988), 155-157. MR 0995423
[4] Robertson A., Robertson W.: Topological vector spaces. Cambridge Univ. Press, 1973. MR 0350361 | Zbl 0423.46001
[5] Schaefer H.: Topological vector spaces. Springer-Verlag, New York-Heidelberg-Berlin, 1971. MR 0342978 | Zbl 0983.46002

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