On sequences in vector lattices. (English) Zbl 0852.46005

Jakubík, Ján

Math. Bohem. 120, No. 4, 379-385 (1995).

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