11. A totally ordered set ( with its order topology ) which is a complete lattice is compact. 12. Hence, considering complete lattices with complete semilattice morphisms boils down to considering Galois connections as morphisms. 13. In 1986, Serra further generalized MM, this time to a theoretical framework based on complete lattices . 14. Complete lattices and orders with a least element ( the " empty supremum " ) provide further examples.15. The set of all such functions forms a complete lattice under the operations of elementwise minimization and maximization. 16. Scott approaches his derivation using a complete lattice , resulting in a topology dependent on the lattice structure. 17. More specific complete lattices are complete Boolean algebras and complete Heyting algebras ( " locales " ). 18. The Dedekind-MacNeille completion is the smallest complete lattice with " S " embedded in it. 19. Nevertheless, the literature on occasion still takes complete join-or meet-semilattices to be complete lattices . 20. Among all possible lattice completions, the Dedekind MacNeille completion is the smallest complete lattice with embedded in it.
