Subgroups and products of $\mathbb {R}$-factorizable $P$-groups

Constancio Hernández; Mihail G. Tkachenko

The Lindelöf property and pseudo- $ℵ_{1}$ -compactness in spaces and topological groups

Constancio Hernández, Mihail G. Tkachenko (2008)

Commentationes Mathematicae Universitatis Carolinae

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We introduce and study, following Z. Frol’ık, the class $ℬ (𝒫)$ of regular $P$ -spaces $X$ such that the product $X \times Y$ is pseudo- $ℵ_{1}$ -compact, for every regular pseudo- $ℵ_{1}$ -compact $P$ -space $Y$ . We show that every pseudo- $ℵ_{1}$ -compact space which is locally $ℬ (𝒫)$ is in $ℬ (𝒫)$ and that every regular Lindelöf $P$ -space belongs to $ℬ (𝒫)$ . It is also proved that all pseudo- $ℵ_{1}$ -compact $P$ -groups are in $ℬ (𝒫)$ . The problem of characterization of subgroups of $ℝ$ -factorizable (equivalently, pseudo- $ℵ_{1}$ -compact) $P$ -groups is considered as well. We...

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