# Continuous images of Lindelöf $p$-groups, $\sigma $-compact groups, and related results

Commentationes Mathematicae Universitatis Carolinae (2019)

- Volume: 60, Issue: 4, page 463-471
- ISSN: 0010-2628

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topArhangel'skii, Aleksander V.. "Continuous images of Lindelöf $p$-groups, $\sigma $-compact groups, and related results." Commentationes Mathematicae Universitatis Carolinae 60.4 (2019): 463-471. <http://eudml.org/doc/295070>.

@article{Arhangelskii2019,

abstract = {It is shown that there exists a $\sigma $-compact topological group which cannot be represented as a continuous image of a Lindelöf $p$-group, see Example 2.8. This result is based on an inequality for the cardinality of continuous images of Lindelöf $p$-groups (Theorem 2.1). A closely related result is Corollary 4.4: if a space $Y$ is a continuous image of a Lindelöf $p$-group, then there exists a covering $\gamma $ of $Y$ by dyadic compacta such that $|\gamma |\le 2^\omega $. We also show that if a homogeneous compact space $Y$ is a continuous image of a $cdc$-group $G$, then $Y$ is a dyadic compactum (Corollary 3.11).},

author = {Arhangel'skii, Aleksander V.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Lindelöf $p$-group; homogeneous space; Lindelöf $\Sigma $-space; dyadic compactum; countable tightness; $\sigma $-compact; $cdc$-group; $p$-space},

language = {eng},

number = {4},

pages = {463-471},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Continuous images of Lindelöf $p$-groups, $\sigma $-compact groups, and related results},

url = {http://eudml.org/doc/295070},

volume = {60},

year = {2019},

}

TY - JOUR

AU - Arhangel'skii, Aleksander V.

TI - Continuous images of Lindelöf $p$-groups, $\sigma $-compact groups, and related results

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2019

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 60

IS - 4

SP - 463

EP - 471

AB - It is shown that there exists a $\sigma $-compact topological group which cannot be represented as a continuous image of a Lindelöf $p$-group, see Example 2.8. This result is based on an inequality for the cardinality of continuous images of Lindelöf $p$-groups (Theorem 2.1). A closely related result is Corollary 4.4: if a space $Y$ is a continuous image of a Lindelöf $p$-group, then there exists a covering $\gamma $ of $Y$ by dyadic compacta such that $|\gamma |\le 2^\omega $. We also show that if a homogeneous compact space $Y$ is a continuous image of a $cdc$-group $G$, then $Y$ is a dyadic compactum (Corollary 3.11).

LA - eng

KW - Lindelöf $p$-group; homogeneous space; Lindelöf $\Sigma $-space; dyadic compactum; countable tightness; $\sigma $-compact; $cdc$-group; $p$-space

UR - http://eudml.org/doc/295070

ER -

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