Complete $\aleph_0$-bounded groups need not be $\Bbb R$-factorizable
Tkachenko, Mihail G.
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 551-559 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We present an example of a complete $\aleph_0$-bounded topological group $H$ which is not $\Bbb R$-factorizable. In addition, every $G_\delta$-set in the group $H$ is open, but $H$ is not Lindelöf.

Publié le : 2001-01-01
Classification:  22A05,  54D20,  54G10,  54G20,  54H11 
@article{119270,
     author = {Mihail G. Tkachenko},
     title = {Complete $\aleph\_0$-bounded groups need not be $\Bbb R$-factorizable},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {551-559},
     zbl = {1053.54045},
     mrnumber = {1860244},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119270}
}

Tkachenko, Mihail G. Complete $\aleph_0$-bounded groups need not be $\Bbb R$-factorizable. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 551-559. http://gdmltest.u-ga.fr/item/119270/

Guran I. On topological groups close to being Lindelöf, Soviet Math. Dokl. 23 (1981), 173-175. (1981) | Zbl 0478.22002

Jech T. Lectures in set theory, Lectures Notes in Math. 217, Berlin, 1971. | Zbl 0269.02030

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) | MR 1001546

Tkachenko M.G. Subgroups, quotient groups and products of $\Bbb R$-factorizable groups, Topology Proc. 16 (1991), 201-231. (1991) | MR 1206464

Tkachenko M.G. Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37. (1991) | MR 1093863 | Zbl 0722.54039

Tkachenko M.G. Introduction to topological groups, Topology Appl. 86 (1998), 179-231. (1998) | MR 1623960 | Zbl 0955.54013

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. | MR 0776623 | Zbl 0769.54008