Ultrafilters on measurable semigroups

Abstract

Let $(S,\cdot )$ be a semigroup and $\mathfrak{m}$ be a $\sigma$-algebra on $S$. We say $(S,\cdot ,\mathfrak{m})$ is a measurable semigroup if $\pi :S\times S⟶S$ by $\pi (x,y)=x\cdot y$ is a measurable function. In this paper , we consider to ${\mathfrak{m}}^{\beta }$ as the collection of all ultrafilters on $\mathfrak{m}$. We show that ${\mathfrak{m}}^{\beta }$ is a compact right topological semigroup respect to generated topology by $\sigma$-algebra $\mathfrak{m}$ on ${\mathfrak{m}}^{\beta }$. Also we study some elementary properties of the algebraic structure of ${\mathfrak{m}}^{\beta }$.

14 pages

References in corpus (1)

• $Lmc-$compactification of a semitopological semigroup as a space of e-ultrafilters