Geodesic
Regulator convergence in commutative $l$-groups
Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 279-284.

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In the theory of lattice ordered groups there are considered several types of convergence. In this work it is shown that for nets ($r$)-convergence is essentially stronger than ($o$)-convergence, while for sequences these notions are not comparable (as is known, in $K$-lineals, ($r$)-convergence for sequences as well as for nets is stronger than ($o$)-convergence); in $K_\sigma$-groups ($r$)-convergence of sequences is stronger than ($o$)-convergence. (A sequence is considered ($o$)-convergent if it is compressed by monotone sequences to a common limit.) 
@article{MZM_1968_3_3_a5,
     author = {\`E. E. Gurevich},
     title = {Regulator convergence in commutative $l$-groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {279--284},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a5/}
}
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È. E. Gurevich. Regulator convergence in commutative $l$-groups. Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 279-284. http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a5/