de las Obras-L.y Nasarre, M. Carmen On the weak convergences and their topologies. (Spanish. English summary) Zbl 0658.46015 Rev. R. Acad. Cienc. Exactas Fís. Nat. Madr. 81, No. 4, 649-654 (1987). Given a real separable Hilbert space H, we denote with G(H) the geometry of the closed linear spaces of H, with \(S=\{E^{(n)}| n\in N\}^ a \)sequence in G(H) and with [C] the closed linear hull of the set C. In previous papers we have defined and characterized the weak convergence in G(H), \(E^{(n)}\rightharpoonup E\), \(E^{(n)}\rightharpoonup^{a}E\), \(E^{(n)}\rightharpoonup^{b}E\). Now we report a topological characterization of these convergences by the weak topology \(\tau_ W\) and the finest topology with the weak convergence, \(\tau_ C\). MSC: 46C99 Inner product spaces and their generalizations, Hilbert spaces 06C20 Complemented modular lattices, continuous geometries Keywords:geometry of the closed linear spaces; weak convergence; topological characterization; weak topology PDFBibTeX XMLCite \textit{M. C. de las Obras-L. y Nasarre}, Rev. R. Acad. Cienc. Exactas Fís. Nat. Madr. 81, 649--654 (1987; Zbl 0658.46015)