{"paper":{"title":"On feebly compact topologies on the semilattice $\\exp_n\\lambda$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Oleg Gutik, Oleksandra Sobol","submitted_at":"2016-06-01T18:51:19Z","abstract_excerpt":"We study feebly compact topologies $\\tau$ on the semilattice $\\left(\\exp_n\\lambda,\\cap\\right)$ such that $\\left(\\exp_n\\lambda,\\tau\\right)$ is a semitopological semilattice. All compact semilattice $T_1$-topologies on $\\exp_n\\lambda$ are described. Also we prove that for an arbitrary positive integer $n$ and an arbitrary infinite cardinal $\\lambda$ for a $T_1$-topology $\\tau$ on $\\exp_n\\lambda$ the following conditions are equivalent: $(i)$ $\\left(\\exp_n\\lambda,\\tau\\right)$ is a compact topological semilattice; $(ii)$ $\\left(\\exp_n\\lambda,\\tau\\right)$ is a countably compact topological semilatt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00395","kind":"arxiv","version":5},"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"}