A note on closed graph theorems. (English) Zbl 1164.46301

Gach, F.

Acta Math. Univ. Comen., New Ser. 75, No. 2, 209-218 (2006).

A bornological closed graph theorem is presented that generalizes the one of N. Popa [C. R. Acad. Sci. Paris, Sér. A 273, 294–297 (1971; Zbl 0217.44401)] and even implies the one of M. De Wilde [Bull. Soc. R. Sci. Liège 40, 116–118 (1971; Zbl 0216.41003)]. It was shown that there is a connection between topological webs in the sense of M. De Wilde and bornological webs on locally convex spaces.

Reviewer: Miloslav Duchoň (Bratislava)

MSC:

46A30	Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46A17	Bornologies and related structures; Mackey convergence, etc.

Keywords:

De Wilde’s closed graph theorem; bornological closed graph theorem; closed graph theorem; convex bornological spaces; webbed locally convex spaces

Citations:

Zbl 0217.44401; Zbl 0216.41003