Geodesic
Lattice normed lattices
Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 2, pp. 280-296

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The topological and order properties of the lattice normed lattices (LNL) with monotonically complete and order semicontinuous norm, taking their values in extended Kantorovich – Pinsker spaces, are studied. It is proved the “vector” variant of Abramovich theorem, giving the criterion of $(bo)$-completeness of LNL. 
@article{DVMG_2014_14_2_a13,
     author = {V. I. Chilin and M. M. Yusupova},
     title = {Lattice normed lattices},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {280--296},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2014_14_2_a13/}
}
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V. I. Chilin; M. M. Yusupova. Lattice normed lattices. Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 2, pp. 280-296. http://geodesic.mathdoc.fr/item/DVMG_2014_14_2_a13/