Lokaltopologische Vektorraume.
In this paper it is proved that if and are two sequences of infinite-dimensional Banach spaces then is not -complete. If and are also reflexive spaces there is on a separated locally convex topology , coarser than the initial one, such that is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on -completeness and bornological spaces.
The paper contains various results concerning the so-called homogeneity sets for convex functions defined on convex subsets of some special metric spaces named G-space (cf. H. Busemann [1]). A closed graph theorem for such type mappings is also presented.