Geodesic
Monotone σ-complete groups with unbounded refinement
Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 177-187

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $∑_ma_m = ∑_nb_n$ 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 large cardinality) satisfying all the above listed axioms except linear ordering.
DOI : 10.4064/fm-151-2-177-187
Keywords: monotone σ-complete groups, partially ordered vector spaces, Archimedean condition

Friedrich Wehrung 1

1 
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Friedrich  Wehrung. Monotone σ-complete groups with unbounded refinement. Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 177-187. doi: 10.4064/fm-151-2-177-187

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