{"paper":{"title":"Connected and/or topological group pd-examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Istvan Juh\\'asz, Jan van Mill, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2017-05-07T13:35:23Z","abstract_excerpt":"The pinning down number $pd(X)$ of a topological space $X$ is the smallest cardinal $\\kappa$ such that for every neighborhood assignment $\\mathcal{U}$ on $X$ there is a set of size $\\kappa$ that meets every member of $\\mathcal{U}$. Clearly, $pd(X) \\le d(X)$ and we call $X$ a pd-example if $pd(X) < d(X)$. We denote by $\\mathbf{S}$ the class of all singular cardinals that are not strong limit. It was proved in a paper of Juh\\'asz,Soukup and Szentmikl\\'ossy (arXiv:1506.00206}) that TFAE:\n  (1) $\\mathbf{S} \\ne \\emptyset$;\n  (2) there is a 0-dimensional $T_2$ pd-example;\n  (3) there is a $T_2$ pd-e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02622","kind":"arxiv","version":1},"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"}