arXiv subjects

A. Pashapournia

Publications and source records attributed to A. Pashapournia.

2 recordsLinked to original sources

arXiv2022

Some Combinatorial Concepts near an Idempotent

A small part of real line which is very close to zero has rich combinatorial properties. The aim of this paper is to express and then prove some locally combinatorial concepts near a virtual idempotent by considering the $wap$-compactification of a semitopological semigroup $S$. The $wap-$compactification of a semitopological semigroup $S$, is denoted by $S^w$, the collection of all ultrafilters near an idempotent $η\in S^w$ forms a compact subsemigroup of $βS_d$, where $S_d$ denotes $S$ as discrete space.

math.FA↗

arXiv2019

Ultrafilters on measurable semigroups

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

math.FA↗