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Sequential convergence on lattice ordered groups. (English) Zbl 0681.06007

The author has studied sequential convergences on abelian lattice ordered groups in his previous paper [ibid. 37(112), 533-546 (1987; Zbl 0645.06006)]. When dealing with the non-abelian case, only an obvious modification of the definition of convergence is needed. Let G be a lattice ordered group and let Conv G be a system of all sequential convergences on G; the system Conv G is partially ordered by inclusion. In the present paper it is proved that Conv G is a lower semilattice and that each interval of Conv G is a complete Brouwerian lattice. If Conv G is upward-directed, then it has a greatest element (and hence it is a complete lattice). For an abelian lattice ordered group G a constructive description of the atoms of Conv G is given.
Reviewer: J.Jakubik

MSC:

06F15 Ordered groups
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces

Citations:

Zbl 0645.06006
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References:

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