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On $B_{r}$ -completeness

Manuel Valdivia (1975)

Annales de l'institut Fourier

In this paper it is proved that if ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are two sequences of infinite-dimensional Banach spaces then $H = (\oplus_{n = 1}^{\infty} E_{n}) \times \prod_{n = 1}^{\infty} F_{n}$ is not $B_{r}$ -complete. If ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are also reflexive spaces there is on $H$ a separated locally convex topology $ℱ$ , coarser than the initial one, such that $H [ℱ]$ is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on $B_{r}$ -completeness and bornological spaces.

On closed graph theorems in topological spaces and groups

Marek Wilhelm (1979)

Fundamenta Mathematicae

On Congruences and Cones.

J. Lawson, Bernard Madison (1971)

Mathematische Zeitschrift

On exhaustive vector measures.

Ferrando, Juan Carlos, López-Pellicer, Manuel (1994)

Revista Colombiana de Matemáticas

On homomorphisms, open operators and their adjoints.

Zarnadze, D. (2001)

Georgian Mathematical Journal

On Inductive Limits of Banach Spaces.

Manuel Valdivia (1975)

Manuscripta mathematica

On Pták's Generalization of the Open-Mapping and Closed-Graph Theorems.

Carl L. DeVito (1988)

Mathematische Zeitschrift

On quasi-completeness and sequential completeness in locally convex spaces.

Manuel Valdivia (1975)

Journal für die reine und angewandte Mathematik

On sequentially retractive inductive limits.

García, Armando (2003)

International Journal of Mathematics and Mathematical Sciences

On some aspects of Jensen-Menger convexity.

Joanna Ger, Roman Ger (1992)

Stochastica

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.