Full lattice convergence on Riesz spaces

2021-05-01
Aydın, Abdullah
Emelyanov, Eduard
Gorokhova, Svetlana
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.
INDAGATIONES MATHEMATICAE-NEW SERIES

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Citation Formats
A. Aydın, E. Emelyanov, and S. Gorokhova, “Full lattice convergence on Riesz spaces,” INDAGATIONES MATHEMATICAE-NEW SERIES, pp. 658–690, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/90694.