{"paper":{"title":"First countable and almost discretely Lindel\\\"of $T_3$ spaces have cardinality at most continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Istv\\'an Juh\\'asz, Lajos Soukup, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2016-12-20T13:29:09Z","abstract_excerpt":"A topological space $X$ is called almost discretely Lindel\\\"of if every discrete set $D \\subset X$ is included in a Lindel\\\"of subspace of $X$. We say that the space $X$ is {\\em $\\mu$-sequential} if for every non-closed set $A \\subset X$ there is a sequence of length $\\le \\mu$ in $A$ that converges to a point which is not in $A$. With the help of a technical theorem that involves elementary submodels, we establish the following two results concerning such spaces.\n  (1) For every almost discretely Lindel\\\"of $T_3$ space $X$ we have $|X| \\le 2^{\\chi(X)}$.\n  (2) If $X$ is a $\\mu$-sequential $T_2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06651","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"}