# Topological type of weakly closed subgroups in Banach spaces

Tadeusz Dobrowolski; Janusz Grabowski; Kazuhiro Kawamura

Studia Mathematica (1996)

- Volume: 118, Issue: 1, page 49-62
- ISSN: 0039-3223

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topDobrowolski, Tadeusz, Grabowski, Janusz, and Kawamura, Kazuhiro. "Topological type of weakly closed subgroups in Banach spaces." Studia Mathematica 118.1 (1996): 49-62. <http://eudml.org/doc/216263>.

@article{Dobrowolski1996,

abstract = {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 $ℓ^1$ which are interesting from the Banach space theory point of view are discussed.},

author = {Dobrowolski, Tadeusz, Grabowski, Janusz, Kawamura, Kazuhiro},

journal = {Studia Mathematica},

keywords = {additive subgroup of linear space; weakly closed; topological dimension; complete Erdős space; Lelek fan; additive subgroups; separable reflexive Banach spaces; complete Erdös space},

language = {eng},

number = {1},

pages = {49-62},

title = {Topological type of weakly closed subgroups in Banach spaces},

url = {http://eudml.org/doc/216263},

volume = {118},

year = {1996},

}

TY - JOUR

AU - Dobrowolski, Tadeusz

AU - Grabowski, Janusz

AU - Kawamura, Kazuhiro

TI - Topological type of weakly closed subgroups in Banach spaces

JO - Studia Mathematica

PY - 1996

VL - 118

IS - 1

SP - 49

EP - 62

AB - 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 $ℓ^1$ which are interesting from the Banach space theory point of view are discussed.

LA - eng

KW - additive subgroup of linear space; weakly closed; topological dimension; complete Erdős space; Lelek fan; additive subgroups; separable reflexive Banach spaces; complete Erdös space

UR - http://eudml.org/doc/216263

ER -

## References

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- [KOT] K. Kawamura, L. G. Oversteegen and E. D. Tymchatyn, On homogeneous totally disconnected 1-dimensional spaces, Fund. Math., to appear. Zbl0861.54028
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