Some aspects of the theory of barreled spaces. (English) Zbl 0656.46001

Perez Carreras, Pedro

Čas. Pěstování Mat. 112, 123-161 (1987).

This is an expository article in which certain aspects of the theory of barreled spaces are discussed. Recent results concerning the problem about conditions on spaces assuring continuity of mappings between them which have closed graph are presented. Further, if a metrizable barreled space is the union of a nondecreasing sequence of closed absolutely convex sets then at least one of them is a neighbourhood of the origin. Recent research related to this property is analysed as well as the question of preservation of barreledness in projective tensor products.

MSC:

46A08	Barrelled spaces, bornological spaces
46A30	Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46M05	Tensor products in functional analysis

Keywords:

\(B_ r\) complete space; Baire space; barreled spaces; closed graph; barreledness in projective tensor products