Том 71
№ 11

All Issues

Petrenko O. V.

Articles: 1
Article (English)

Balleans and G -spaces

Petrenko O. V., Protasov I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 344-350

We show that every ballean (equivalently, coarse structure) on a set $X$ can be determined by some group $G$ of permutations of $X$ and some group ideal $\mathcal{I}$ on $G$. We refine this characterization for some basic classes of balleans: metrizable, cellular, graph, locally finite, and uniformly locally finite. Then we show that a free ultrafilter $\mathcal{U}$ on $\omega$ is a $T$-point with respect to the class of all metrizable locally finite balleans on $\omega$ if and only if $\mathcal{U}$ is a $Q$-point. The paper is concluded with а list of open questions.