{"paper":{"title":"Talagrand compacta, 2DCP, and pointwise quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jerzy K\\k{a}kol, Tomasz Kania","submitted_at":"2026-07-07T21:14:22Z","abstract_excerpt":"We revisit Talagrand's CH compactum as a test object for the two-disjoint-copies property and for pointwise quotient questions. The two-disjoint-copies property, or 2DCP, is a topological sufficient condition for the existence of infinite-dimensional metrisable quotients of spaces $C_{\\operatorname{p}}(X)$; recent work asks whether Talagrand's compactum has this property. Assuming $\\diamondsuit(S)$ for a stationary co-stationary $S\\subseteq\\omega_1$, we carry out Talagrand's inverse-limit construction with additional diagonalisation. The resulting compactum $T$ keeps Talagrand's conclusions: $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06808","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/2607.06808/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"}