Abstract
Abstract We prove that a completely regular locale L is realcompact if and only if the “remainder” β L ∖ L {\beta L\smallsetminus L} is the join of the zero-sublocales of β L {\beta L} that miss L. This extends a result of Mrówka which characterizes realcompact spaces in terms of their remainders in Stone–Čech compactifications. We prove that β L ∖ L {\beta L\smallsetminus L} is Lindelöf if and only if L is of countable type, where the latter is defined for locales exactly as for spaces, subject to replacing subspaces with sublocales.
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 callSimilar Papers
Disclaimer: 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.
