Full lattice convergence on Riesz spaces

AYDIN A., EMELYANOV E., Gorokhova S.

INDAGATIONES MATHEMATICAE-NEW SERIES, vol.32, no.3, pp.658-690, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1016/j.indag.2021.01.008
  • Journal Name: INDAGATIONES MATHEMATICAE-NEW SERIES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.658-690
  • Keywords: Riesz space, f-algebra, Full convergence, Lattice convergence, Unbounded c-convergence, Multiplicative c-convergence, UO-CONVERGENCE, VALUED MODELS, F-ALGEBRAS
  • Middle East Technical University Affiliated: Yes

Abstract

The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications of a full convergence c on a Riesz space. The first one produces a sequential convergence sc. The second makes an absolute c-convergence and generalizes the absolute weak convergence. The third modification makes an unbounded c-convergence and generalizes various unbounded convergences recently studied in the literature. The last one is applicable whenever c is a full convergence on a commutative l-algebra and produces the multiplicative modification mc of c. We study general properties of full lattice convergence with emphasis on universally complete Riesz spaces and on Archimedean f -algebras. The technique and results in this paper unify and extend those which were developed and obtained in recent literature on unbounded convergences.