Displaying similar documents to “The Lindelöf property and pseudo-$\aleph_1$-compactness in spaces and topological groups”

Subgroups and products of ℝ -factorizable P -groups

Constancio Hernández, Mihail G. Tkachenko (2004)

Commentationes Mathematicae Universitatis Carolinae

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We show that subgroup of an ℝ -factorizable abelian P -group is topologically isomorphic to a 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...

Subgroups of ℝ -factorizable groups

Constancio Hernández, Mihail G. Tkachenko (1998)

Commentationes Mathematicae Universitatis Carolinae

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The properties of ℝ -factorizable groups and their subgroups are studied. We show that a locally compact group G is ℝ -factorizable if and only if G is σ -compact. It is proved that a subgroup H of an ℝ -factorizable group G is ℝ -factorizable if and only if H is z -embedded in G . Therefore, a subgroup of an ℝ -factorizable group need not be ℝ -factorizable, and we present a method for constructing non- ℝ -factorizable dense subgroups of a special class of ℝ -factorizable groups. Finally, we construct...