Ultracompanions of subsets of a group

Abstract

Let $G$ be a group, $\beta G$ is the Stone-$\check{C}$ech compactification of $\beta G$ endowed with the structure of a right topological semigroup, $G^{\ast }=\beta G\setminus G$. Given any subset $A$ of $G$ and $p\in G^{\ast }$, we define the $p$-companion $\vt_p(A)=A^*\cap Gp$ of $A$, and characterize the subsets with finite and discrete ultracompanions.

References in corpus (2)

• The Solecki submeasures and densities on groups
• Asymptotically Scattered Spaces

Cited by in corpus (1)

• Relative size of subsets of a semigroup