I. Banakh

activity

20102023

most citedOn Local Convexity Of Nonlinear Mappings Between Banach Spaces

2 citations · 4 across the 10 of their papers we have counts for

collaborators

12 papers

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.MG2023

Metric characterizations of some subsets of the real line

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A metric space $(X, d)$ is called a $s u b l in e$ if every 3-element subset $T$ of $X$ can be written as $T = {x, y, z}$ for some points $x, y, z$ such that $d (x, z) = d (x, y) + d (y, z)$ . By a cla…

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.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.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 completion of the hyperspace of finite subsets, endowed with the $ℓ^{1}$ -metric

Iryna Banakh, Taras Banakh, Joanna Garbulińska-Wȩgrzyn

For a metric space $X$ , let $F X$ be the space of all nonempty finite subsets of $X$ endowed with the largest metric $d_{F X}^{1}$ such that for every $n \in N$ t…

math.GN2020

On the asymptotic dimension of products of coarse spaces

Iryna Banakh, Taras Banakh

We prove that for any coarse spaces $X_{1}, \dots, X_{n}$ of asymptotic dimension $\geq 1$ , the product $X = X_{1} \times \dots \times X_{n}$ has asymptotic dimension $\geq n$ . Another result state…

math.GN2018

The continuity of Darboux injections between manifolds

Iryna Banakh, Taras Banakh

We prove that an injective map $f : X \to Y$ between connected metrizable spaces $X, Y$ is continuous if for every connected subset $C \subset X$ the image $f (C)$ is connected and one o…

math.GN2017

The connected countable spaces of Bing and Ritter are topologically homogeneous

Iryna Banakh, Taras Banakh, Olena Hryniv +1

Answering a problem posed by the second author on Mathoverflow, we prove that the connected countable Hausdorff spaces constructed by Bing and Ritter are topologically homogeneous.

math.FA2012★ 2 cited

On Local Convexity Of Nonlinear Mappings Between Banach Spaces

Iryna Banakh, Taras Banakh, Anatolij Plichko +1

We find conditions for a smooth nonlinear map $f : U \to V$ between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some $c$ and each posit…

q-fin.GN2012★ 1 cited

Toehold Purchase Problem: A comparative analysis of two strategies

Iryna Banakh, Taras Banakh, Pavel Trisch +1

Toehold purchase, defined here as purchase of one share in a firm by an investor preparing a tender offer to acquire majority of shares in it, reduces by one the number of shares t…

math.FA2010★ 1 cited

Constructing non-compact operators into $c_{0}$

Iryna Banakh, Taras Banakh

We prove that for each dense non-compact linear operator $S : X \to Y$ between Banach spaces there is a linear operator $T : Y \to c_{0}$ such that the operator $T S : X \to c_{0}$ is not compac…

Midconvex sets in Abelian groups

Metric characterizations of some subsets of the real line

Semiaffine sets in Abelian groups

On symmetrizability and perfectness of second-countable spaces

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

The completion of the hyperspace of finite subsets, endowed with the ℓ1-metric

On the asymptotic dimension of products of coarse spaces

The continuity of Darboux injections between manifolds

The connected countable spaces of Bing and Ritter are topologically homogeneous

On Local Convexity Of Nonlinear Mappings Between Banach Spaces

Toehold Purchase Problem: A comparative analysis of two strategies

Constructing non-compact operators into c0​

The completion of the hyperspace of finite subsets, endowed with the $ℓ^{1}$ -metric

Constructing non-compact operators into $c_{0}$