Ultrafilters on metric spaces (Q2435275)

In this paper, the author's main aim is to reveal some features of algebra in \(\beta X\) similar to the algebra in the Stone--Čech compactification of a discrete semigroup. The main results are that: (1) the author characterizes a small subset and asymptotically scattered subsets of a space in term of their ultracompanions; (2) the author shows that from the ballean point of view the minimal closed invariant subsets are counterparts of the minimal left ideals in \(\beta G\), where \(G\) is a discrete group.