A Banach-Dieudonné theorem for the space of bounded continuous functions on a separable metric space with the strict topology (Q2630449)

This paper investigates locally convex properties of the space of bounded continuous functions on a separable metric topological space \(X\) endowed with the strict topology of Buck and Sentilles. The author proves a Banach-Dieudonné-type result, and obtains versions of closed graph and open mapping theorems. Reviewer's remark: Unfortunately, the author seems to ignore the important work of \textit{W. Ruess} about (gDF)-spaces in which he exploited the rich locally convex structure of strict topologies. See, for example, the papers [Math. Z. 153, 179--192 (1977; Zbl 0361.46002); Math. Proc. Camb. Philos. Soc. 82, 67--83 (1977; Zbl 0361.46001)] that are very relevant in connection with the research of the paper under review.