{"paper":{"title":"Some new results on well-filteredness of $T_0$-spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Xiaoquan Xu","submitted_at":"2026-06-17T08:08:56Z","abstract_excerpt":"For a $T_0$-space $X$, let $Q (X)$ be the poset of nonempty compact saturated sets of $X$ with the reverse inclusion order. The space $X$ is said to have property Q if it satisfies the following two conditions: (1) $\\wedge K$ exists for any $K\\in Q(X)$, and (2) for any filtered family $\\{K_d : d\\in D\\}\\subseteq Q(X)$ and $x\\in X$, if $\\bigvee^{\\uparrow}_{d\\in D}\\bigwedge K_d$ exists and $x\\not\\leq \\bigvee^{\\uparrow}_{d\\in D}\\bigwedge K_d$, then there is $\\varphi\\in \\prod\\limits_{d\\in D}\\!\\!K_d$ and an upper bound $u$ of $\\varphi(D)$ such that $x\\not\\leq u$. In this paper, we prove that every $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18796","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18796/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}