| 1. | It remains to be proven that P is a complete lattice.
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| 2. | Every poset that is a complete semilattice is also a complete lattice.
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| 3. | The posets with this property are the complete lattices.
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| 4. | :" Let L be a complete lattice and let f : L ?
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| 5. | Some authors work even with more general structures than the real line, like complete lattices.
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| 6. | L be an fixed points of f in L is also a complete lattice ."
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| 7. | The subsequent generalization to complete lattices is widely accepted today as MM's theoretical foundation.
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| 8. | Complete lattices are partially ordered sets, where every subset has an infimum and a supremum.
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| 9. | The set of all clones is a closure system, hence it forms a complete lattice.
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| 10. | This method is used, for example, in the proof that there is no complete lattice.
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