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Topological type of weakly closed subgroups in Banach spaces. (English) Zbl 0856.46012

Summary: 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 Erdös space. Two examples of such subgroups in \(\ell^1\) which are interesting from the Banach space theory point of view are discussed.

MSC:

46B25 Classical Banach spaces in the general theory
54F45 Dimension theory in general topology
22A05 Structure of general topological groups
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