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Complete 0 -bounded groups need not be -factorizable

Mihail G. Tkachenko (2001)

Commentationes Mathematicae Universitatis Carolinae

We present an example of a complete 0 -bounded topological group H which is not -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.

Connected LCA groups are sequentially connected

Shou Lin, Mihail G. Tkachenko (2013)

Commentationes Mathematicae Universitatis Carolinae

We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if H is a connected locally compact Abelian subgroup of a Hausdorff topological group G and the quotient space G / H is sequentially connected, then so is G .

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