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