Majorizing-injectivity in abelian lattice-ordered groups
Maximal convergences and minimal proper convergences in -groups
Maximal Dedekind completion of an abelian lattice-ordered group
Monotone σ-complete groups with unbounded refinement
The real line ℝ may be characterized as the unique non-atomic directed partially ordered abelian group which is monotone σ-complete (countable increasing bounded sequences have suprema), has the countable refinement property (countable sums of positive (possibly infinite) elements have common refinements) and is linearly ordered. We prove here that the latter condition is not redundant, thus solving an old problem by A. Tarski, by proving that there are many spaces (in particular, of arbitrarily...