The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in which are interesting from the Banach space theory point of view are discussed.
@article{bwmeta1.element.bwnjournal-article-smv118i1p49bwm, author = {Tadeusz Dobrowolski and Janusz Grabowski and Kazuhiro Kawamura}, title = {Topological type of weakly closed subgroups in Banach spaces}, journal = {Studia Mathematica}, volume = {119}, year = {1996}, pages = {49-62}, zbl = {0856.46012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i1p49bwm} }
Dobrowolski, Tadeusz; Grabowski, Janusz; Kawamura, Kazuhiro. Topological type of weakly closed subgroups in Banach spaces. Studia Mathematica, Tome 119 (1996) pp. 49-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i1p49bwm/
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