Closed Left Ideal Decompositions of $U(G)$

Canadian mathematical bulletin

Yevhen Zelenyuk¹ 

[1]School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa

关键词: Stone--Čech compactification;    uniform ultrafilter;    closed left ideal;    decomposition;   

DOI  :  10.4153/CMB-2011-175-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $G$ be an infinite discrete group and let $eta G$ be theStone--Čech compactification of $G$. We take the points of $ėtaG$ to be the ultrafilters on $G$, identifying the principalultrafilters with the points of $G$. The set $U(G)$ of uniformultrafilters on $G$ is a closed two-sided ideal of $eta G$. Forevery $pin U(G)$, define $I_psubseteqeta G$ by $I_p=igcap_{Ainp}operatorname{cl} (GU(A))$, where $U(A)={pin U(G):Ain p}$. We showthat if $|G|$ is a regular cardinal, then ${I_p:pin U(G)}$ is thefinest decomposition of $U(G)$ into closed left ideals of $eta G$such that the corresponding quotient space of $U(G)$ is Hausdorff.

【 授权许可】

Unknown