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Displaying similar documents to “Subgroups of ℝ -factorizable groups”

Cellularity and the index of narrowness in topological groups

Mihail G. Tkachenko (2011)

Commentationes Mathematicae Universitatis Carolinae

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We study relations between the cellularity and index of narrowness in topological groups and their G δ -modifications. We show, in particular, that the inequalities in ( ( H ) τ ) ≤ 2 τ · in ( H ) and c ( ( H ) τ ) ≤ 2 2 τ · in ( H ) hold for every topological group H and every cardinal τ ≥ ω , where ( H ) τ denotes the underlying group H endowed with the G τ -modification of the original topology of H and in ( H ) is the index of narrowness of the group H . Also, we find some bounds for the complexity of continuous real-valued functions f on an arbitrary ω -narrow group...

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...

The dual group of a dense subgroup

William Wistar Comfort, S. U. Raczkowski, F. Javier Trigos-Arrieta (2004)

Czechoslovak Mathematical Journal

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Throughout this abstract, G is a topological Abelian group and G ^ is the space of continuous homomorphisms from G into the circle group 𝕋 in the compact-open topology. A dense subgroup D of G is said to determine G if the (necessarily continuous) surjective isomorphism G ^ ↠ D ^ given by h ↦ h | D is a homeomorphism, and G is determined if each dense subgroup of G determines G . The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable...

Metrization criteria for compact groups in terms of their dense subgroups

Dikran Dikranjan, Dmitri Shakhmatov (2013)

Fundamenta Mathematicae

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According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or G δ -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined...