Full lattice convergence on Riesz spaces - Aydin, Abdullah; Emelyanov, Eduard; Gorokhova, Svetlana (Elsevier B.V., 2021)
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. © 2021 Royal Dutch Mathematical Society (KWG)
2-s2.0-85101696039
Keywords: f-algebra; Full convergence; Lattice convergence; Multiplicative c-convergence; Riesz space; Unbounded c-convergence