{"paper":{"title":"A compact group which is not Valdivia compact","license":"","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Vladimir Uspenskij, Wieslaw Kubi\\'s","submitted_at":"2003-11-03T03:28:15Z","abstract_excerpt":"A compact space $K$ is {\\em Valdivia compact} if it can be embedded in a Tikhonov cube $I^A$ in such a way that the intersection $K\\cap\\Sigma$ is dense in $K$, where $\\Sigma$ is the sigma-product (= the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight $\\o_1$ which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311015","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"}