{"paper":{"title":"$u\\tau$-Convergence in locally solid vector lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"E. Yu. Emelyanov, M. A. A. Marabeh, Y. A. Dabboorasad","submitted_at":"2017-06-06T23:39:29Z","abstract_excerpt":"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 $\\lvert x_\\alpha-x \\rvert\\wedge w \\xrightarrow{\\tau} 0$ 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. Besides, we introduce $u\\tau$-topology and study briefly metrizabililty and completeness of this topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02006","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}