Complete ℵ 0 -bounded groups need not be ℝ -factorizable

Mihail G. Tkachenko

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 3, page 551-559
  • ISSN: 0010-2628

Abstract

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We present an example of a complete ℵ 0 -bounded topological group H which is not ℝ -factorizable. In addition, every G δ -set in the group H is open, but H is not Lindelöf.

How to cite

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Tkachenko, Mihail G.. "Complete $\aleph _0$-bounded groups need not be $\mathbb {R}$-factorizable." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 551-559. <http://eudml.org/doc/248810>.

@article{Tkachenko2001,
abstract = {We present an example of a complete $\aleph _0$-bounded topological group $H$ which is not $\mathbb \{R\}$-factorizable. In addition, every $G_\delta $-set in the group $H$ is open, but $H$ is not Lindelöf.},
author = {Tkachenko, Mihail G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\mathbb \{R\}$-factorizable group; $\aleph _0$-bounded group; $P$-group; complete; Lindelöf; -factorizable group; -bounded group; -group; complete; Lindelöf},
language = {eng},
number = {3},
pages = {551-559},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Complete $\aleph _0$-bounded groups need not be $\mathbb \{R\}$-factorizable},
url = {http://eudml.org/doc/248810},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Tkachenko, Mihail G.
TI - Complete $\aleph _0$-bounded groups need not be $\mathbb {R}$-factorizable
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 551
EP - 559
AB - We present an example of a complete $\aleph _0$-bounded topological group $H$ which is not $\mathbb {R}$-factorizable. In addition, every $G_\delta $-set in the group $H$ is open, but $H$ is not Lindelöf.
LA - eng
KW - $\mathbb {R}$-factorizable group; $\aleph _0$-bounded group; $P$-group; complete; Lindelöf; -factorizable group; -bounded group; -group; complete; Lindelöf
UR - http://eudml.org/doc/248810
ER -

References

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  1. Guran I., On topological groups close to being Lindelöf, Soviet Math. Dokl. 23 (1981), 173-175. (1981) Zbl0478.22002
  2. Jech T., Lectures in set theory, Lectures Notes in Math. 217, Berlin, 1971. Zbl0269.02030
  3. Tkachenko M.G., Generalization of a theorem of Comfort and Ross, Ukrainian Math. J. 41 (1989), 334-338; Russian original in Ukrain. Mat. Zh. 41 (1989), 377-382. (1989) MR1001546
  4. Tkachenko M.G., Subgroups, quotient groups and products of ℝ -factorizable groups, Topology Proc. 16 (1991), 201-231. (1991) MR1206464
  5. Tkachenko M.G., Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37. (1991) Zbl0722.54039MR1093863
  6. Tkachenko M.G., Introduction to topological groups, Topology Appl. 86 (1998), 179-231. (1998) Zbl0955.54013MR1623960
  7. Williams S.W., Box products, in Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan, eds., Chapter 4, North-Holland, Amsterdam, 1984, pp.169-200. Zbl0769.54008MR0776623

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