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Keywords:
$\Bbb R$-factorizable group; $\aleph_0$-bounded group; $P$-group; complete; Lindelöf
Summary:
We present an example of a complete $\aleph_0$-bounded topological group $H$ which is not $\Bbb R$-factorizable. In addition, every $G_\delta$-set in the group $H$ is open, but $H$ is not Lindelöf.
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