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Keywords:
semilattice; lattice; distributive; dimension group; direct limit
semilattice; lattice; distributive; dimension group; direct limit
Summary:
We construct a countable chain of Boolean semilattices, with all inclusion maps preserving the join and the bounds, whose union cannot be represented as the maximal semilattice quotient of the positive cone of any dimension group. We also construct a similar example with a countable chain of strongly distributive bounded semilattices. This solves a problem of F. Wehrung.
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