Local Polarity

Let  be a lattice, and let . Then the pair  is a local polarity if and only if for each finite set , there is a finitely generated sublattice  of  that contains  and on which the restriction  is a lattice polarity.

Using nonstandard methods, one may show that the following result holds: Let  be a locally finite lattice. Then the set of local polarities of  is a relation  which is a one-to-one correspondence between its domain and range.

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