Homomorphic images of -factorizable groups

Mihail G. Tkachenko

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 525-537
  • ISSN: 0010-2628

Abstract

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It is well known that every -factorizable group is ω -narrow, but not vice versa. One of the main problems regarding -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every ω -narrow group is a continuous homomorphic image of an -factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an -factorizable group is a P -group, then the image is also -factorizable.

How to cite

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Tkachenko, Mihail G.. "Homomorphic images of $\mathbb {R}$-factorizable groups." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 525-537. <http://eudml.org/doc/249869>.

@article{Tkachenko2006,
abstract = {It is well known that every $\mathbb \{R\}$-factorizable group is $\omega $-narrow, but not vice versa. One of the main problems regarding $\mathbb \{R\}$-factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every $\omega $-narrow group is a continuous homomorphic image of an $\mathbb \{R\}$-factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an $\mathbb \{R\}$-factorizable group is a $P$-group, then the image is also $\mathbb \{R\}$-factorizable.},
author = {Tkachenko, Mihail G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\mathbb \{R\}$-factorizable; totally bounded; $\omega $-narrow; complete; Lindelöf; $P$-space; realcompact; Dieudonné-complete; pseudo-$\omega _1$-compact; totally bounded; -narrow; complete; Lindelöf; -space},
language = {eng},
number = {3},
pages = {525-537},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Homomorphic images of $\mathbb \{R\}$-factorizable groups},
url = {http://eudml.org/doc/249869},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Tkachenko, Mihail G.
TI - Homomorphic images of $\mathbb {R}$-factorizable groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 525
EP - 537
AB - It is well known that every $\mathbb {R}$-factorizable group is $\omega $-narrow, but not vice versa. One of the main problems regarding $\mathbb {R}$-factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every $\omega $-narrow group is a continuous homomorphic image of an $\mathbb {R}$-factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an $\mathbb {R}$-factorizable group is a $P$-group, then the image is also $\mathbb {R}$-factorizable.
LA - eng
KW - $\mathbb {R}$-factorizable; totally bounded; $\omega $-narrow; complete; Lindelöf; $P$-space; realcompact; Dieudonné-complete; pseudo-$\omega _1$-compact; totally bounded; -narrow; complete; Lindelöf; -space
UR - http://eudml.org/doc/249869
ER -

References

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