{"paper":{"title":"Continuity of the Jones' set function $\\mathcal{T}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Carlos Uzcategui, Javier Camargo","submitted_at":"2015-11-22T22:58:16Z","abstract_excerpt":"Given a continuum $X$, for each $A\\subseteq X$, the Jones' set function $\\mathcal{T}$ is defined by $\\mathcal{T}(A)=\\{x\\in X : \\text{for each subcontinuum }K\\text{ such that }x\\in \\textrm{Int}(K), \\text{ then }K\\cap A\\neq\\emptyset\\}.$ We show that $\\mathcal{D}=\\{\\mathcal{T}(\\{x\\}):x\\in X\\}$ is decomposition of $X$ when $\\mathcal{T}$ is continuous. We present a characterization of the continuity of $\\mathcal{T}$ and answer several open questions posed by D. Bellamy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07083","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"}