Abstract
In this paper, we introduce and study strongly semicontinuous lattices, a new class of complete lattices lying between the class of semicontinuous lattices and that of continuous lattices. It is shown that a complete lattice L is strongly semicontinuous iff L is semicontinuous and meet semicontinuous. Some versions of strong interpolation properties for the semiway-below relation in (strongly) semicontinuous lattices are established. Characterization theorems by some distributivity and approximate identities for strongly semicontinuous lattices are given, which reveals that strongly semicontinuous lattices indeed share similar properties with continuous lattices. A subtle counterexample is constructed to show that semicontinuous lattices need not be strongly semicontinuous lattices.
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.
