On Metric Completness and Completness in sense of Lattices

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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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Functional Analysis, Classical Analysis and ODEs, 46E05 (primary); 06B30 (secondary); 46A40; 54H12

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http://salesiana.dossiersoluciones.com/handle/123456789/69678

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312410
 http://arxiv.org/abs/math/0312410

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arXiv