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 2023Show all

5 papers · 1 filter

math.CO2023

Game extensions of floppy graph metrics

Taras Banakh, Pietro Majer

A $g r a p h$ $m e t r i c$ on a set $X$ is any function $d : E_{d} \to R_{+} := {x \in R : x > 0}$ defined on a connected graph $E_{d} \subseteq [X]^{2} := {A \subseteq X : ∣ A ∣ = 2}$ and such t…

math.GN2023★ 1 cited

Banakh spaces and their geometry

Taras Banakh

Following Will Brian, we define a metric space $X$ to be $B anak h$ if all nonempty spheres of positive radius $r$ in $X$ have cardinality $2$ and diameter $2 r$ . Standard examples of…

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 $G$ …