{"paper":{"title":"Wijsman hyperspaces of non-separable metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Paul Szeptycki, Rodrigo Hern\\'andez-Guti\\'errez","submitted_at":"2013-12-05T21:12:59Z","abstract_excerpt":"Given a metric space $\\langle X,\\rho \\rangle$, consider its hyperspace of closed sets $CL(X)$ with the Wijsman topology $\\tau_{W(\\rho)}$. It is known that $\\langle{CL(X),\\tau_{W(\\rho)}}\\rangle$ is metrizable if and only if $X$ is separable and it is an open question by Di Maio and Meccariello whether this is equivalent to $\\langle{CL(X),\\tau_{W(\\rho)}}\\rangle$ being normal. In this paper we prove that if the weight of $X$ is a regular uncountable cardinal and $X$ is locally separable, then $\\langle{CL(X),\\tau_{W(\\rho)}}\\rangle$ is not normal. We also solve some questions by Cao, Junnilla and M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1705","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"}