T. Banakh

activity

20062025

most citedEmbedding the bicyclic semigroup into countably compact topological semigroups

33 citations · 687 across the 231 of their papers we have counts for

collaborators

Showing 2020Show all

18 papers · 1 filter

math.GR2020★ 1 cited

Weak completions of paratopological groups

Taras Banakh, Mikhail Tkachenko

Given a $T_{0}$ paratopological group $G$ and a class $C$ of continuous homomorphisms of paratopological groups, we define the $C$ - $se mi co m pl e t i o n$ $C [G)$ …

math.GR2020

A semigroup is finite if and only if it is chain-finite and antichain-finite

Iryna Banakh, Taras Banakh, Serhii Bardyla

A subset $A$ of a semigroup $S$ is called a $c hain$ ( $an t i c hain$ ) if $x y \in {x, y}$ ( $x y \in / {x, y}$ ) for any (distinct) elements $x, y \in S$ . A semigroup $S$ is called ( $an t i$ )$c…

math.GN2020

The Set-Cover game and nonmeasurable unions

Taras Banakh, Robert Rałowski, Szymon Żeberski

Using a game-theoretic approach we present a generalization of the classical result of Brzuchowski, Cichoń, Grzegorek and Ryll-Nardzewski on non-measurable unions. We also present…

math.GN2020

On unconditionally convergent series in topological rings

Taras Banakh, Alex Ravsky

We define a topological ring $R$ to be \emph{Hirsch}, if for any unconditionally convergent series $\sum_{n \in ω} x_{i}$ in $R$ and any neighborhood $U$ of the additive identity $0$ o…

math.GN2020

$ω^{ω}$ -Base and infinite-dimensional compact sets in locally convex spaces

Taras Banakh, Jerzy Kąkol, Johannes Phillip Schürz

A locally convex space (lcs) $E$ is said to have an $ω^{ω}$ -base if $E$ has a neighborhood base ${U_{α} : α \in ω^{ω}}$ at zero such that $U_{β} \subseteq U_{α}$ for all $α \leq β$ . The class of…

math.GN2020★ 5 cited

The Kirch space is topologically rigid

Taras Banakh, Yaryna Stelmakh, Sławomir Turek

The $G o l o mb$ $s p a ce$ (resp. the $K i r c h$ $s p a ce$ ) is the set $N$ of positive integers endowed with the topology generated by the base consisting of arithmetic progressions $…

Weak completions of paratopological groups

A semigroup is finite if and only if it is chain-finite and antichain-finite

The Set-Cover game and nonmeasurable unions

On unconditionally convergent series in topological rings

ωω-Base and infinite-dimensional compact sets in locally convex spaces

The Kirch space is topologically rigid

$ω^{ω}$ -Base and infinite-dimensional compact sets in locally convex spaces