Lattice ordered groups with unique addition must be archimedean
Lattice-ordered groups with rank one components
Les cônes autopolaires en dimension finie
Les sous-groupes d'un groupe quasi-réticulé
Lexico extension and a cut completion of a half l-group
The cut completi on of an hl-group G with the abelian increasing part is investigated under the assumption that G is a lexico extension of its hl-subgroup.
Lexicographic product decompositions of cyclically ordered groups
Local/global uniform approximation of real-valued continuous functions
For a Tychonoff space , is the lattice-ordered group (-group) of real-valued continuous functions on , and is the sub--group of bounded functions. A property that might have is (AP) whenever is a divisible sub--group of , containing the constant function 1, and separating points from closed sets in , then any function in can be approximated uniformly over by functions which are locally in . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...
Locally conditioned radical classes of lattice-ordered groups
Locally finite conditions on lattice-ordered groups
Locally solid topological lattice-ordered groups
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered group is...
Lorenzen's theorem for pseudo-effect algebras
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...
Nearly disjoint sequences in convergence -groups
For an abelian lattice ordered group let be the system of all compatible convergences on ; this system is a meet semilattice but in general it fails to be a lattice. Let be the convergence on which is generated by the set of all nearly disjoint sequences in , and let be any element of . In the present paper we prove that the join does exist in .
Normalization of -algebras
We consider algebras determined by all normal identities of -algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a -lattice, and another one based on a normalization of a lattice-ordered group.
Notes per a un estudi de la geometría sobre grups involutius.
On absolute retracts and absolute convex retracts in some classes of l-groups
By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.
On adjoining units to hyper-archimedean -groups