More on ordinals in topological groups
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 127-140
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Let $\tau$ be an uncountable regular cardinal and $G$ a $T_1$ topological group. We prove the following statements: (1) If $\tau$ is homeomorphic to a closed subspace of $G$, $G$ is Abelian, and the order of every non-neutral element of $G$ is greater than $5$ then $\tau\times\tau$ embeds in $G$ as a closed subspace. (2) If $G$ is Abelian, algebraically generated by $\tau\subset G$, and the order of every element does not exceed $3$ then $\tau\times \tau$ is not embeddable in $G$. (3) There exists an Abelian topological group $H$ such that $\omega_1$ is homeomorphic to a closed subspace of $H$ and $\{t^2:t\in T\}$ is not closed in $H$ whenever $T\subset H$ is homeomorphic to $\omega_1$. Some other results are obtained.
@article{CMUC_2008__49_1_a11,
author = {Arhangel'skii, Aleksander V. and Buzyakova, Raushan Z.},
title = {More on ordinals in topological groups},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {127--140},
publisher = {mathdoc},
volume = {49},
number = {1},
year = {2008},
mrnumber = {2433630},
zbl = {1212.54103},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a11/}
}
TY - JOUR AU - Arhangel'skii, Aleksander V. AU - Buzyakova, Raushan Z. TI - More on ordinals in topological groups JO - Commentationes Mathematicae Universitatis Carolinae PY - 2008 SP - 127 EP - 140 VL - 49 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a11/ LA - en ID - CMUC_2008__49_1_a11 ER -
Arhangel'skii, Aleksander V.; Buzyakova, Raushan Z. More on ordinals in topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 127-140. http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a11/