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On Metric Completness and Completness in sense of Lattices

Serguei Samborski
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Abstract

We give an answer to the following question: for which metric in an abstract lattice the completion as a metric space coincides with the completion as a lattice. We obtain the answer for inductive limits of lattices which are complete in both senses. As an application we construct such a metric in the lattice of continuous functions endowed with the uniform convergence.

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Serguei Samborski. 2004-05-18. On Metric Completness and Completness in sense of Lattices. https://arxiv.org/abs/math/0312410

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