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Closed subgroups in Banach spaces

Fredric Ancel, Tadeusz Dobrowolski, Janusz Grabowski (1994)

Studia Mathematica

We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of c 0 . Other results on subgroups of linear spaces are obtained.

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

Mihail G. Tkachenko (2001)

Commentationes Mathematicae Universitatis Carolinae

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.

Condensations of Tychonoff universal topological algebras

Constancio Hernández (2001)

Commentationes Mathematicae Universitatis Carolinae

Let ( L , 𝒯 ) be a Tychonoff (regular) paratopological group or algebra over a field or ring K or a topological semigroup. If nw ( L , 𝒯 ) ≤ τ and nw ( K ) ≤ τ , then there exists a Tychonoff (regular) topology 𝒯 * ⊆ 𝒯 such that w ( L , 𝒯 * ) ≤ τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.

Continuous actions of pseudocompact groups and axioms of topological group

Alexander V. Korovin (1992)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class 𝒩 of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces 𝒩 that gives some new examples and statements for the C p -theory and theory of topologically homogeneous spaces.

Countable dense homogeneous filters and the Menger covering property

Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang (2014)

Fundamenta Mathematicae

We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n ∈ ω ∪ {∞} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.

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