Abstract
It is shown that atomic block-finite orthomodular lattices (OMLs) belong to the class of OMLs the MacNeille completion of which is an OML. Further, it is shown that a complete block-finite OML is atomic iff the interval topology on it is Hausdorff, and that a complete (o)-continuous commutator-finite and irreducible OML is atomic. Finally, compact topological OMLs are studied and some equivalent conditions under which they are profinite (i.e., isomorphic with a direct product of finite OMLs) are found.
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.
