On Metric Completness and Completness in sense of Lattices
Serguei Samborski · arXiv (Cornell University) · 2003
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.