## 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

### Keywords:

pseudo-order; trellis; complete trellis
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