Strictly webbed spaces and regularity properties of inductive limits. (Q5957252)

The purpose of this paper is to show that sequentially complete, locally complete, locally Baire, and bornivorously webbed are equivalent for strictly webbed spaces and for inductive limits of strictly webbed spaces. Unfortunately there are serious doubts that the proofs of Theorems 2.2 and 3.2 are correct. They are based on an argument taken from Theorem 1 in \textit{C. Bosch} and \textit{J. Kučera} [Czech. Math. J. 52, No. 2, 329--332 (2002; Zbl 1075.46502)], which is false. In my opinion, the equivalence between sequentially complete and locally complete, in the context of this paper, is still open. On the other hand Lemma 2.1 is less general than a result of M. Valdivia (see 9.1.43 in \textit{J. Bonet} and \textit{P. Pérez-Carreras} [Barrelled locally convex spaces. North-Holland Mathematics Studies, 131. Amsterdam etc.: North-Holland (1987; Zbl 0614.46001)]).