{"paper":{"title":"Path connectedness, local path connectedness and contractibility of $\\mathcal{S}_c(X)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"David Maya, Javier Camargo, Patricia Pellicer-Covarrubias","submitted_at":"2018-02-02T15:15:38Z","abstract_excerpt":"The hyperspace of all nontrivial convergent sequences in a Hausdorff space $X$ is denoted by $\\mathcal{S}_c(X)$. This hyperspace is endowed with the Vietoris topology. In connection with a question and a problem by Garc\\'ia-Ferreira, Ortiz-Castillo and Rojas-Hern\\'andez, concerning conditions under which $\\mathcal S_c(X)$ is pathwise connected, in the current paper we study the latter property and the contractibility of $\\mathcal{S}_c(X)$. We present necessary conditions on a space $X$ to obtain the path connectedness of $\\mathcal{S}_c(X)$. We also provide some sufficient conditions on a space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00725","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"}