{"paper":{"title":"Lonely points revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jonathan L. Verner","submitted_at":"2016-07-21T11:36:04Z","abstract_excerpt":"In our previous paper, Lonely points, we introduced the notion of a lonely point, due to P. Simon. A point $p\\in X$ is lonely if it is a limit point of a countable dense-in-itself set, not a limit point a countable discrete set and all countable sets whose limit point it is, form a filter. We use the space ${\\mathcal G}_\\omega$ from a paper of A. Dow, A.V. Gubbi and A. Szyma\\'nski (Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745--748) to construct lonely points in $\\omega^*$. This answers the question of P. Simon posed in our paper Lonely points (Lonely points in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06273","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"}