A countably cellular topological group all of whose countable subsets are closed need not be -factorizable
Commentationes Mathematicae Universitatis Carolinae (2023)
- Volume: 64, Issue: 1, page 127-135
- ISSN: 0010-2628
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topTkachenko, Mihail G.. "A countably cellular topological group all of whose countable subsets are closed need not be $\mathbb {R}$-factorizable." Commentationes Mathematicae Universitatis Carolinae 64.1 (2023): 127-135. <http://eudml.org/doc/299577>.
@article{Tkachenko2023,
abstract = {We construct a Hausdorff topological group $G$ such that $\aleph _1$ is a precalibre of $G$ (hence, $G$ has countable cellularity), all countable subsets of $G$ are closed and $C$-embedded in $G$, but $G$ is not $\mathbb \{R\}$-factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.},
author = {Tkachenko, Mihail G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\mathbb \{R\}$-factorizable; cellularity; $C$-embedded; Sorgenfrey line; $P$-group; Dieudonné completion; Hewitt–Nachbin completion; Bohr topology},
language = {eng},
number = {1},
pages = {127-135},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A countably cellular topological group all of whose countable subsets are closed need not be $\mathbb \{R\}$-factorizable},
url = {http://eudml.org/doc/299577},
volume = {64},
year = {2023},
}
TY - JOUR
AU - Tkachenko, Mihail G.
TI - A countably cellular topological group all of whose countable subsets are closed need not be $\mathbb {R}$-factorizable
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 1
SP - 127
EP - 135
AB - We construct a Hausdorff topological group $G$ such that $\aleph _1$ is a precalibre of $G$ (hence, $G$ has countable cellularity), all countable subsets of $G$ are closed and $C$-embedded in $G$, but $G$ is not $\mathbb {R}$-factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.
LA - eng
KW - $\mathbb {R}$-factorizable; cellularity; $C$-embedded; Sorgenfrey line; $P$-group; Dieudonné completion; Hewitt–Nachbin completion; Bohr topology
UR - http://eudml.org/doc/299577
ER -
References
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