I. Protasov

activity

20102021

most citedAlgebraically determined topologies on permutation groups

16 citations · 84 across the 49 of their papers we have counts for

collaborators

64 papers

math.GN2021

On a question of Clark and Ledet

Igor Protasov

Given a $T$ -sequence on a countable abelian group $G$ , we prove that there exists $2^{2^{∣ G ∣}}$ Hausdorff group topologies in which this sequence converges to $0$ . This answers a q…

math.GN2021

On asymorphisms of finitary coarse spaces

I. V. Protasov

We characterize finitary coarse spaces $X$ such that every permutation of $X$ is an asymorphism.

math.GN2021

Linearly ordered coarse spaces

Igor Protasov

A coarse space $X$ , endowed with a linear order compatible with the coarse structure of $X$ , is called linearly ordered. We prove that every linearly ordered coarse space $X$ is lo…

math.GN2021

Coarse selectors of graphs

Igor Protasov

We consider a connected graph $Γ$ as a coarse space and prove that $Γ$ admits a 2-selector if and only if $Γ$ is either bounded or coarsely equivalent to $N$ or $\mathbb{Z…

math.GR2021

Coarse selectors of groups

Igor Protasov

For a group $G$ , $F_{G}$ denotes the set of all non-empty finite subsets of $G$ . We extend the finitary coarse structure of $G$ from $G \times G$ to $\mathcal{F}_G\times \ma…

math.GN2021

Selectors and orderings of coarse spaces

Igor Protasov

Given a coarse space $(X, E)$ , we consider linear orders on $X$ compatible with the coarse structure $E$ and explore interplays between these orders and macro-un…