{"paper":{"title":"On $\\mathcal{B}$-Open Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Layth M. Alabdulsada","submitted_at":"2019-05-01T21:54:09Z","abstract_excerpt":"The aim of this paper is to define and study $\\mathcal{B}$-open sets and related properties. A $\\mathcal{B}$-open set is, roughly speaking, a generalization of a $b$-open set, which is in turn a generalization of a pre-open set and a semi-open set. Using $\\mathcal{B}$-open sets, we introduce a number of concepts such as $\\mathcal{B}$-dense, $\\mathcal{B}$-Frechet, contra-$\\mathcal{B}$-closed graph and contra-$\\mathcal{B}$-continuity. Also, we define a bi-operator topological space $(X, \\tau, T_1, T_2)$ which involves two operators $T_1$ and $T_2$, which are used to define $\\mathcal{B}$-open set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00513","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"}