Abstract
AbstractSome filter relative notions of size, $$\left( \mathscr {F},\mathscr {G}\right) $$ F , G -syndeticity and piecewise $$\mathscr {F} $$ F -syndeticity, were defined and applied with clarity and focus by Shuungula, Zelenyuk and Zelenyuk (Semigroup Forum 79: 531–539, 2009). These notions are generalizations of the well studied notions of syndeticity and piecewise syndeticity. Since then, there has been an effort to develop the theory around the algebraic structure of the Stone–Čech compactification so that it encompasses these new generalizations. We prove one direction of a characterization of piecewise $$\mathscr {F}$$ F -syndetic sets. This completes the characterization, as the other direction was proved by Christopherson and Johnson (Semigroup Forum 104: 28–44, 2021).
Sign-in/Register to access full text options 
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.
