{"paper":{"title":"Strongly Hit and Far Miss Hypertopology and Hit and Strongly Far Miss Hypertopology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"C. Guadagni, J.F. Peters","submitted_at":"2015-03-09T17:56:13Z","abstract_excerpt":"This article introduces the {\\it strongly hit and far-miss as well as hit and strongly far miss hypertopologies on $\\textrm{CL}(X)$ associated with} ${\\mathscr{B}}$, a nonempty family of subsets on the topological space $X$. They result from the strong farness and strong nearness proximities. The main results in this paper stem from the Hausdorffness of $(\\textrm{CL}(X), \\tau_{\\doublevee, \\mathscr{B}})$ and $(\\textrm{RCL}(X), \\tau^\\doublewedge_\\mathscr{B} ) $, where $\\textrm{RCL}(X)$ is the space of regular closed subsets of $X$. To obtain the results, special local families are introduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02587","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"}