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u tau-convergence in locally solid vector lattices

Dabboorasad, Y. A.
Emelyanov, Eduard
Marabeh, M. A. A.
Let be a net in a locally solid vector lattice ; we say that is unbounded -convergent to a vector if 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.