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

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Showing 2022Show all

14 papers · 1 filter

math.GR2022★ 2 cited

A non-polybounded absolutely closed $36$ -Shelah group

Taras Banakh

For every infinite cardinal $κ$ with $κ^{+} = 2^{κ}$ we construct a group $G$ of cardinality $∣ G ∣ = κ^{+}$ such that (i) $G$ is $36$ -Shelah, which means that $A^{36} = G$ for any subset $A\sub…

math.GR2022

Polyboundedness of zero-closed semigroups

Taras Banakh, Andriy Rega

The polyboundedness number $cov (A_{X})$ of a semigroup $X$ is the smallest cardinality of a cover of $X$ by sets of the form ${x \in X : a_{0} x a_{1} \dots x a_{n} = b}$ for s…

math.GN2022

Examples of strongly rigid countable (semi)Hausdorff spaces

Taras Banakh, Yaryna Stelmakh

A topological space $X$ is $s t r o n g l y$ $r i g i d$ if each non-constant continuous map $f : X \to X$ is the identity map of $X$ . A Hausdorff topological space $X$ is called $B r o w n$ if for…

math.GR2022

Subgroups of categorically closed semigroups

Taras Banakh, Serhii Bardyla

Let $C$ be a class of topological semigroups. A semigroup $X$ is called (1) $C$ - $c l ose d$ if $X$ is closed in every topological semigroup $Y \in C$ containi…

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.GN2022

Injectively and absolutely $T_{1} S$ -closed semigroups

Taras Banakh

A semigroup $X$ is $ab so l u t e l y$ (resp. $inj ec t i v e l y$ ) $T_{1} S$ - $c l ose d$ if for any (injective) homomorphism $h : X \to Y$ to a $T_{1}$ topological semigroup $Y \in C$ , the image $h…

math.GN2022

Categorically closed unipotent semigroups

Taras Banakh, Myroslava Vovk

Let $C$ be a class of $T_{1}$ topological semigroups, containing all Hausdorff zero-dimensional topological semigroups. A semigroup $X$ is $C$ - $c l ose d$ if $X$ is cl…

math.GN2022

Automatic continuity of measurable homomorphisms on Cech-complete topological groups

Taras Banakh

We prove that a homomorphism $h : X \to Y$ from a (locally compact) Cech-complete topological group $X$ to a topological group $Y$ is continuous if and only if $h$ is Borel-measurable…

math.GN2022

Absolutely closed semigroups

Taras Banakh, Serhii Bardyla

Let $C$ be a class of topological semigroups. A semigroup $X$ is called $ab so l u t e l y$ $C$ - $c l ose d$ if for any homomorphism $h : X \to Y$ to a topological semigroup $Y…

math.GN2022

First-countable Lindelöf scattered spaces

Taras Banakh, Will Brian, Alejandro Ríos-Herrejón

We study the class of first-countable Lindelöf scattered spaces, or "FLS" spaces. While every $T_{3}$ FLS space is homeomorphic to a scattered subspace of $Q$ , the class of $…

math.GN2022

On symmetrizability and perfectness of second-countable spaces

Iryna Banakh, Taras Banakh, Lidiya Bazylevych

A symmetrizability criterion of Arhangelskii implies that a second-countable Hausdorff space is symmetrizable if and only if it is perfect. We present an example of a non-symmetriz…

math.GN2022

$Q$ -spaces, perfect spaces and related cardinal characteristics of the continuum

Taras Banakh, Lidiya Bazylevych

A topological space $X$ is called a $Q$ -space if every subset of $X$ is of type $F_{σ}$ in $X$ . For $i \in {1, 2, 3}$ let $q_{i}$ be the smallest cardinality of a second-counta…

math.GR2022

The binary quasiorder on semigroups

Taras Banakh, Olena Hryniv

Given two elements $x, y$ of a semigroup $X$ we write $x ≲ y$ if for every homomorphism $χ : X \to {0, 1}$ we have $χ (x) \leq χ (y)$ . The quasiorder $≲$ is called the $bina r y$ …

math.RA2022

$E$ -separated semigroups

Taras Banakh

A semigroup is called $E$ - $se p a r a t e d$ if for any distinct idempotents $x, y \in X$ there exists a homomorphism $h : X \to Y$ to a semilattice $Y$ such that $h (x) \neq = h (y)$ . Developing re…

A non-polybounded absolutely closed 36-Shelah group

Polyboundedness of zero-closed semigroups

Examples of strongly rigid countable (semi)Hausdorff spaces

Subgroups of categorically closed semigroups

Injectively closed commutative semigroups

Injectively and absolutely T1​S-closed semigroups

Categorically closed unipotent semigroups

Automatic continuity of measurable homomorphisms on Cech-complete topological groups

Absolutely closed semigroups

First-countable Lindelöf scattered spaces

On symmetrizability and perfectness of second-countable spaces

Q-spaces, perfect spaces and related cardinal characteristics of the continuum

The binary quasiorder on semigroups

E-separated semigroups

A non-polybounded absolutely closed $36$ -Shelah group

Injectively and absolutely $T_{1} S$ -closed semigroups

$Q$ -spaces, perfect spaces and related cardinal characteristics of the continuum

$E$ -separated semigroups