Regulator convergence in commutative $l$-groups

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.)