Geodesic
On Metric Completeness and Order Completeness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 228-236 
S. N. Samborskii. On Metric Completeness and Order Completeness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 228-236. http://geodesic.mathdoc.fr/item/TM_2004_247_a15/
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     author = {S. N. Samborskii},
     title = {On {Metric} {Completeness} and {Order} {Completeness}},
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     url = {http://geodesic.mathdoc.fr/item/TM_2004_247_a15/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A positive answer to the question of whether there exists a metric on the lattice of continuous functions that generates uniform convergence and is such that the metric completion is simultaneously the order completion is given. Two interpretations of the obtained metric lattice are suggested.

[1] Birkgof G., Teoriya reshetok, Nauka, M., 1984 | MR

[2] Neubrunn T., “Quasi-continuity”, Real Anal. Exchange, 14:2 (1989), 259–306 | MR | Zbl

[3] Samborskii S. N., “O rasshireniyakh differentsialnykh operatorov i negladkikh resheniyakh differentsialnykh uravnenii”, Kibernetika i sistemnyi analiz, 2002, no. 3, 163–180 | MR | Zbl