On Metric Completness and Completness in sense of Lattices
Functional Analysis
2007-05-23 v2 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.math/0312410,
title = {On Metric Completness and Completness in sense of Lattices},
author = {Serguei Samborski},
journal= {arXiv preprint arXiv:math/0312410},
year = {2007}
}
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