Convergences and complete distributivity of lattice ordered groups
Ján Jakubík · Czech digital mathematics library · 1988
JAN JAKUBIK C J. Everett and S. Ulam [2] investigated the order convergence of sequences in an abelian lattice ordered group G.Some other types of convergences in G were studied by F. Papangelou [10].An axiomatic treatement of sequential convergences on G was performed by M. Harminc [3], [4], [5] (in some results of [5] the lattice ordered group G need not be abelian).Higher degrees of distributivity in lattice ordered groups (including complete distributivity) were studied by several authors (cf.e.g., Weinberg [8] and the author [6]).Let ConvG" be the system of all sequential convergences on G (for the definition, cf.below).The system Conv G is partially ordered by inclusion.In [5] it was shown that ConvG need not be a lattice and it was proved (without assuming the commutativity of G) that the following conditions are equivalent:(In the present paper it will be shown that each archimedean completely distributive lattice ordered group satisfies the condition (i).