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We prove that (1) each infinite compact Hausdorff space $X$ contains a non-isolated point $x$ with $nw_\\chi(x)=\\aleph_0$; (2) for each point $x\\in X$ with countable character there is an injective sequence in $X$ that $\\F$-converges to $x$ for some meager filter $\\F$ on $\\omega$; (3) if a functionally Hausdorff space $X$ contains an $\\F$-convergent injective sequenc"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.2522","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-12-12T08:21:44Z","cross_cats_sorted":[],"title_canon_sha256":"8336e1de853531bc65749751b6eb56bd676a6a0cda225cc05e08fccd8c1f9d11","abstract_canon_sha256":"ab93b2e0febd6d576f8896743d4b6a78aaaec9d3f1edfc31406819276a14a348"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:04.173771Z","signature_b64":"Q0iG6Wxk0E67UyPmuJaw+XmURJCqxQMs4J6e7U1eZQP/3STSF7sgui9WFOxcMX2NnySNX4qINR++fIgxrKvxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cb46fda433cb69aad17089d12f664031689d4cfdaa3b2201a39be4f982b1f74","last_reissued_at":"2026-05-18T04:15:04.173159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:04.173159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On meager function spaces, network character and meager convergence in topological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Lyubomyr Zdomskyy, Taras Banakh, Volodymyr Mykhaylyuk","submitted_at":"2010-12-12T08:21:44Z","abstract_excerpt":"For a non-isolated point $x$ of a topological space $X$ the network character $nw_\\chi(x)$ is the smallest cardinality of a family of infinite subsets of $X$ such that each neighborhood $O(x)$ of $x$ contains a set from the family. 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