$$u\tau $$-convergence in locally solid vector lattices

Let \((x_\alpha )\) be a net in a locally solid vector lattice \((X,\tau )\); we say that \((x_\alpha )\) is unbounded \(\tau \)-convergent to a vector \(x\in X\) if \(|x_\alpha -x |\wedge w \xrightarrow {\tau } 0\) for all \(w\in X_+\). In this paper, we study general properties of unbounded \(\tau \)-convergence (shortly \(u\tau \)-convergence). \(u\tau \)-convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. We introduce \(u\tau \)-topology and briefly study metrizability and completeness of this topology.