Displaying similar documents to “Homomorphic images of ℝ -factorizable groups”

Complete ℵ 0 -bounded groups need not be ℝ -factorizable

Mihail G. Tkachenko (2001)

Commentationes Mathematicae Universitatis Carolinae

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We present an example of a complete ℵ 0 -bounded topological group H which is not ℝ -factorizable. In addition, every G δ -set in the group H is open, but H is not Lindelöf.

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...