{"paper":{"title":"Tolerances induced by irredundant coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.RA","authors_text":"Jouni J\\\"arvinen, S\\'andor Radeleczki","submitted_at":"2014-04-21T12:58:38Z","abstract_excerpt":"In this paper, we consider tolerances induced by irredundant coverings. Each tolerance $R$ on $U$ determines a quasiorder $\\lesssim_R$ by setting $x \\lesssim_R y$ if and only if $R(x) \\subseteq R(y)$. We prove that for a tolerance $R$ induced by a covering $\\mathcal{H}$ of $U$, the covering $\\mathcal{H}$ is irredundant if and only if the quasiordered set $(U, \\lesssim_R)$ is bounded by minimal elements and the tolerance $R$ coincides with the product ${\\gtrsim_R} \\circ {\\lesssim_R}$. We also show that in such a case $\\mathcal{H} = \\{ {\\uparrow}m \\mid \\text{$m$ is minimal in $(U,\\lesssim_R)$} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5184","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"}