I. Protasov

activity

20122021

most citedCoarse spaces, ultrafilters and dynamical systems

2 citations · 7 across the 22 of their papers we have counts for

collaborators

Showing 2017 · math.GNShow all

7 papers · 2 filters

math.GN2017

Counting coarse subsets of a countable group

Igor Protasov, Ksenia Protasova

For every countable group $G$ , there are $2^{ω}$ distinct classes of coarsely equivalent subsets of $G$ .

math.GN2017

Metrically Ramsey ultrafilters

Igor Protasov, Ksenia Protasova

Given a metric space $(X, d)$ , we say that a mapping $χ : [X]^{2} ⟶ {0.1}$ is an isometric coloring if $d (x, y) = d (z, t)$ implies $χ ({x, y}) = χ ({z, t})$ . A free ultrafilt…

math.GN2017

Ideals in $P_{G}$ and $β G$

Igor Protasov, Ksenia Protasova

For a discrete group $G$ , we use the natural correspondence between ideals in the Boolean algebra $P_{G}$ of subsets of $G$ and closed subsets in the Stone- $C ˇ$ ech…

math.GN2017

Ramsey-product subsets of a group

Igor Protasov, Ksenia Protasova

We say that a subset $S$ of an infinite group $G$ is a Ramsey-product subset if, for any infinite subsets $X$ , $Y$ of $G$ , there exist $x \in X$ and $y \in Y$ such that $x y \in S$ …

math.GN2017

On recurrence in G-spaces

Igor Protasov, Ksenia Protasova

We introduce and analyze the following general concept of recurrence. Let $G$ be a group and let $X$ be a G-space with the action $G \times X ⟶ X$ , $(g,x)\longmapsto gx…

math.GN2017

The descriptive look at the size of subsets of groups

Igor Protasov, Taras Banakh, Ksenia Protasova

We explore the Borel complexity of some basic families of subsets of a countable group (large, small, thin, sparse and other) defined by the size of their elements. Applying the ob…

Counting coarse subsets of a countable group

Metrically Ramsey ultrafilters

Ideals in PG​ and βG

Ramsey-product subsets of a group

On recurrence in G-spaces

The descriptive look at the size of subsets of groups

Ideals in $P_{G}$ and $β G$