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arXiv · 1706.02006

$uτ$-Convergence in locally solid vector lattices

Y. A. Dabboorasad·E. Yu. Emelyanov·M. A. A. Marabeh
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Abstract

Let $x_α$ be a net in a locally solid vector lattice $(X,τ)$; we say that $x_α$ is unbounded $τ$-convergent to a vector $x\in X$ if $\lvert x_α-x \rvert\wedge w \xrightarrowτ 0$ for all $w\in X_+$. In this paper, we study general properties of unbounded $τ$-convergence (shortly, $uτ$-convergence). $uτ$-Convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. Besides, we introduce $uτ$-topology and study briefly metrizabililty and completeness of this topology.

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BibTeXRIS

Y. A. Dabboorasad, E. Yu. Emelyanov, M. A. A. Marabeh. 2017-06-20. $uτ$-Convergence in locally solid vector lattices. https://arxiv.org/abs/1706.02006

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