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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
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