Full lattice convergence on Riesz spaces

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. (c) 2021 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.