Abstract
AbstractLet G be an infinite discrete group and let βG be the Stone-Čech compactification of G. We take the points of βG to be the ultrafilters on G, identifying the principal ultrafilters with the points of G. The set U(G) of uniform ultrafilters on G is a closed two-sided ideal of βG. For every p ∊ U(G), define Ip ⊆ βG by Ip = ∩ A∊p cl(GU(A)), whereU(A) = {p ∊ U(G) : A ∊ p}. We show that if |G| is a regular cardinal, then {Ip : p ∊ U(G)} is the finest decomposition of U(G) into closed left ideals of βG such that the corresponding quotient space of U(G) is Hausdorff.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
