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Ideal exhaustiveness, continuity and \((\alpha)\)-convergence for lattice group-valued functions. (English) Zbl 1221.28021

Int. J. Pure Appl. Math. 70, No. 2, 211-227 (2011); addendum ibid. 75, No. 3, 383-384 (2012).
Summary: We examine some fundamental properties of \({\mathcal I}\)-exhaustiveness, previously studied in the real case in [Ch. Papachristodoulos, N. Papanastassiou and W. Wilczyński, “\(I\)-exhaustive sequences of functions”, Topology Appl. (to appear)], in the context of \((\ell)\)-groups with respect to \((D)\)-convergence, and we answer to an open problem posed by V. Gregoriades and N. Papanastassiou in [Topology Appl. 155, No. 10, 1111–1128 (2008; Zbl 1141.26001)].

MSC:

28B15 Set functions, measures and integrals with values in ordered spaces
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)

Citations:

Zbl 1141.26001
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