Displaying similar documents to “Complete ℵ 0 -bounded groups need not be ℝ -factorizable”

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 × 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...

Homomorphic images of ℝ -factorizable groups

Mihail G. Tkachenko (2006)

Commentationes Mathematicae Universitatis Carolinae

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It is well known that every ℝ -factorizable group is ω -narrow, but not vice versa. One of the main problems regarding ℝ -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every ω -narrow group is a continuous homomorphic image of an ℝ -factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an ℝ -factorizable...

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...