Now showing items 1-4 of 4

• #### -convergence in locally solid vector lattices

(Springer International Publishing, 2018)
Let be a net in a locally solid vector lattice; we say that is unbounded-convergent to a vector if$$| x_\alpha-x|\wedge w\xrightarrow {\tau} 0$$ for all. In this paper, we study general properties of unbounded-convergence ...
• #### Order convergence in infinite-dimensional vector lattices is not topological

(2017)
In this note, we show that the order convergence in a vector lattice is not topological unless . Furthermore, we show that, in atomic order continuous Banach lattices, the order convergence is topological on order ...
• #### um-Topology in multi-normed vector lattices

(Springer International Publishing, 2018)
Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) ...
• #### Unbounded Convergence in the Convergence Vector Lattices: a Survey

(2018)
on the occas'ion of hi,s 65th anniuersary Various convergences in vector lattices were historicalll' a subject of deep investigation v'hich stems from the begining of the 20th century in works of Riesz, Kantorovich, Nakano, ...