Topological vector spaces. The theory without convexity conditions. (English) Zbl 0397.46005

Adasch, Norbert; Ernst, Bruno; Keim, Dieter

Lecture Notes in Mathematics. 639. Berlin-Heidelberg-New York: Springer-Verlag. 125 p. (1978).

MSC:

46A19	Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)
46A30	Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46A08	Barrelled spaces, bornological spaces
46A04	Locally convex Fréchet spaces and (DF)-spaces
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
46A32	Spaces of linear operators; topological tensor products; approximation properties

Keywords:

Df-Spaces; Barrelled Spaces; Spaces with a Fundamental Sequence Of Compact Sets; Open-Mapping Theorem; Completion; Topological Vector Spaces; Infra-S-Spaces; F-Spaces; Boundedly Summing Spaces; Closed-Graph Theorem; Banach-Steinhaus Theorem; String in a Vector Space; Quasibarrelled Spaces; Spaces of Linear Construous Mappins; Sigma-Locally Topological Spaces