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      -convergence in locally solid vector lattices

      Dabboorasad, Yousef A.m.; Emelyanov, E YU; Marabeh, Maa (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 ...
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      Order convergence in infinite-dimensional vector lattices is not topological

      Dabboorasad, Yousef A.m.; Emelyanov, E YU; Marabeh, Maa (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 ...
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      um-Topology in multi-normed vector lattices

      Dabboorasad, Yousef A.m.; Emelyanov, E YU; Marabeh, Maa (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) ...