{"paper":{"title":"On totally periodic w-limit sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Habib Marzougui, Issam Naghmouchi","submitted_at":"2014-06-17T15:23:14Z","abstract_excerpt":"An w-limit set of a continuous self-mapping of a compact metric space X is said to be totally periodic if all of its points are periodic. We say that X has the w-FTP property provided that for each continuous self-mapping f of X, every totally periodic w-limit set is finite. Firstly, we show that connected components of every totally periodic w-limit set are finite. Secondly, for the wide class of one-dimensional continua, we prove that a hereditary locally connected X has the w-FTP property if and only if X is completely regular. This holds in particular for X being a local dendrite with disc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4401","kind":"arxiv","version":2},"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"}