-convergence in locally solid vector lattices

Abstract

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 (shortly-convergence).-convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. We introduce-topology and briefly study metrizability and completeness of this topology.