Geodesic
On spaces in which the norm convergence coincides with the order convergence
Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 259-268.

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We investigate partially ordered normed vector spaces in which the norm convergence coincides with the order convergence. We consider spaces where the convergences coincide for arbitrary nets and spaces where the convergences coincide only for sequences. We give conditions which characterize such spaces and investigate their properties. In particular, we study the problem of their Dedekind completeness and $\sigma$-completeness. 
@article{MZM_1973_13_2_a10,
     author = {B. Z. Vulikh and O. S. Korsakova},
     title = {On spaces in which the norm convergence coincides with the order convergence},
     journal = {Matemati\v{c}eskie zametki},
     pages = {259--268},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a10/}
}
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B. Z. Vulikh; O. S. Korsakova. On spaces in which the norm convergence coincides with the order convergence. Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 259-268. http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a10/