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On sequences in vector lattices. (English) Zbl 0852.46005
D. E. Peek [Real Anal. Exch. 17, No. 2, 751-758 (1992; Zbl 0759.26006)] investigated a collection $$\sigma= \{\text{A1}- \text{A6}\}$$ of six conditions for systems of sequences of reals.
In the present paper, we deal with a slightly modified collection $$\sigma'$$ of conditions that can be applied for systems of sequences in a vector lattice $$X$$. If $$X= \mathbb{R}$$ (the set of reals), then $$\sigma$$ and $$\sigma'$$ are equivalent.
##### MSC:
 46A40 Ordered topological linear spaces, vector lattices 40A05 Convergence and divergence of series and sequences
##### Keywords:
vector lattice; $$o$$-convergence; Archimedean property
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