Тарас Банах

activity

20102023

most citedOn subgroups of saturated or totally bounded paratopological groups

18 citations · 31 across the 20 of their papers we have counts for

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Showing math.GRShow all

5 papers · 1 filter

math.GR2023

Midconvex sets in Abelian groups

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A subset $X$ of an Abelian group $G$ is called $mi d co n v e x$ if for every $x, y \in X$ the set $\frac{x + y}{2} = {z \in G : 2 z = x + y}$ is a subset of $X$ . We prove that a subset $X$ of an Abel…

math.GR2023

Semiaffine sets in Abelian groups

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A subset $X$ of an Abelian group $G$ is called $se mia f f in e$ if for every $x, y, z \in X$ the set ${x + y - z, x - y + z}$ intersects $X$ . We prove that a subset $X$ of an Abelian group $G$ …

math.GR2022

Injectively closed commutative semigroups

Taras Banakh

Let $C$ be a class of topological semigroups. A semigroup $X$ is $inj ec t i v e l y$ $C$ - $c l ose d$ if $X$ is closed in each topological semigroup $Y \in C$ contai…

math.GR2010

The structure of infinite 2-groups with a unique 2-element subgroup

Taras Banakh

We prove that each infinite 2-group with a unique 2-element subgroup is isomorphic either to the quasicyclic 2-group or to the infinite group of generalized quaternions.

math.GR2010★ 18 cited

On subgroups of saturated or totally bounded paratopological groups

Taras Banakh, Alex Ravsky

A paratopological group $G$ is saturated if the inverse $U^{- 1}$ of each non-empty set $U \subset G$ has non-empty interior. It is shown that a [first-countable] paratopological gro…