engleski

A Topology on Lattice Ordered Groups

We show that a lattice ordered group can be topologized in a natural way. The topology depends on the choice of a set C of admissible elements (C-topology). If a lattice ordered group is 2-divisible and satisfies a version of Archimedes' axiom (C-group), then we show that the C-topology is Hausdorff. Moreover, we show that the C-topology is a topological group.

Lattice ordered group; set of admissible elements; C-topology; C-group

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