On the least complete extension of complete subsemilattices
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For a complete sublattice X of a complete lattice C, we consider the problem of the existence of the least complete meet subsemilattice of C having as least complete extension (i.e., the least complete sublattice of C containing it) X. We argue that this problem is not trivial, and we provide two results that, under certain conditions on C and X, give a positive answer to this problem.
KeywordsPositive Answer Complete Lattice Complete Extension Complete Sublattice
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