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A characterization of completeness for trellises. (English) Zbl 1013.06003

A trellis is defined as a pseudo-ordered set any two of whose elements have a GLB and LUB (a pseudo-order is a reflexive and antisymmetric binary relation). Main result: A trellis \(A\) is complete (i.e. every subset of \(A\) has a GLB and a LUB) if and only if every ascending well-ordered \(p\)-chain in \(A\) has a join.

MSC:

06A06 Partial orders, general
06B23 Complete lattices, completions
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