Algebraic posets, algebraic cpo's and models of concurrency
Topology and category theory in computer science
Handbook of logic in computer science (vol. 3)
Meet continuity properties of posets
Theoretical Computer Science
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In this paper, we introduce the concept of meet precontinuous posets, a generalization of meet continuous lattices to posets. The main results are: (1) A poset P is meet precontinuous iff its normal completion is a meet continuous lattice iff a certain system @c(P) which is, in the case of complete lattices, the lattice of all Scott-closed sets is a complete Heyting algebra; (2) A poset P is precontinuous iff the way below relation is the smallest approximating auxiliary relation iff P is meet precontinuous and there is a smallest approximating auxiliary relation on P. Finally, given a poset P and an auxiliary relation on P, we characterize those join-dense subsets of P whose way-below relation agrees with the given auxiliary relation.