Subgroups and products of ℝ -factorizable P -groups

Constancio Hernández; Mihail G. Tkachenko

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 1, page 153-167
  • ISSN: 0010-2628

Abstract

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We show that every subgroup of an ℝ -factorizable abelian P -group is topologically isomorphic to a closed subgroup of another ℝ -factorizable abelian P -group. This implies that closed subgroups of ℝ -factorizable P -groups are not necessarily ℝ -factorizable. We also prove that if a Hausdorff space Y of countable pseudocharacter is a continuous image of a product X = ∏ i ∈ I X i of P -spaces and the space X is pseudo- ω 1 -compact, then n w ( Y ) ≤ ℵ 0 . In particular, direct products of ℝ -factorizable P -groups are ℝ -factorizable and ω -stable.

How to cite

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Hernández, Constancio, and Tkachenko, Mihail G.. "Subgroups and products of $\mathbb {R}$-factorizable $P$-groups." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 153-167. <http://eudml.org/doc/249344>.

@article{Hernández2004,
abstract = {We show that every subgroup of an $\mathbb \{R\}$-factorizable abelian $P$-group is topologically isomorphic to a closed subgroup of another $\mathbb \{R\}$-factorizable abelian $P$-group. This implies that closed subgroups of $\mathbb \{R\}$-factorizable $P$-groups are not necessarily $\mathbb \{R\}$-factorizable. We also prove that if a Hausdorff space $Y$ of countable pseudocharacter is a continuous image of a product $X=\prod _\{i\in I\}X_i$ of $P$-spaces and the space $X$ is pseudo-$\omega _1$-compact, then $nw(Y)\le \aleph _0$. In particular, direct products of $\mathbb \{R\}$-factorizable $P$-groups are $\mathbb \{R\}$-factorizable and $\omega $-stable.},
author = {Hernández, Constancio, Tkachenko, Mihail G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$P$-space; $P$-group; pseudo-$\omega _1$-compact; $\omega $-stable; $\mathbb \{R\}$-factorizable; $\aleph _0$-bounded; pseudocharacter; cellularity; $\aleph _ 0$-box topology; $\sigma $-product; -space; -group; pseudo--compact; -stable; -factorizable},
language = {eng},
number = {1},
pages = {153-167},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Subgroups and products of $\mathbb \{R\}$-factorizable $P$-groups},
url = {http://eudml.org/doc/249344},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Hernández, Constancio
AU - Tkachenko, Mihail G.
TI - Subgroups and products of $\mathbb {R}$-factorizable $P$-groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 153
EP - 167
AB - We show that every subgroup of an $\mathbb {R}$-factorizable abelian $P$-group is topologically isomorphic to a closed subgroup of another $\mathbb {R}$-factorizable abelian $P$-group. This implies that closed subgroups of $\mathbb {R}$-factorizable $P$-groups are not necessarily $\mathbb {R}$-factorizable. We also prove that if a Hausdorff space $Y$ of countable pseudocharacter is a continuous image of a product $X=\prod _{i\in I}X_i$ of $P$-spaces and the space $X$ is pseudo-$\omega _1$-compact, then $nw(Y)\le \aleph _0$. In particular, direct products of $\mathbb {R}$-factorizable $P$-groups are $\mathbb {R}$-factorizable and $\omega $-stable.
LA - eng
KW - $P$-space; $P$-group; pseudo-$\omega _1$-compact; $\omega $-stable; $\mathbb {R}$-factorizable; $\aleph _0$-bounded; pseudocharacter; cellularity; $\aleph _ 0$-box topology; $\sigma $-product; -space; -group; pseudo--compact; -stable; -factorizable
UR - http://eudml.org/doc/249344
ER -

References

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  13. Tkachenko M., Subgroups, quotient groups and products of ℝ -factorizable groups, Topology Proc. 16 (1991), 201-231. (1991) MR1206464
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