{"paper":{"title":"Marde\\v{s}i\\'c conjecture and free products of Boolean algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Gonzalo Mart\\'inez-Cervantes, Grzegorz Plebanek","submitted_at":"2017-11-28T16:52:25Z","abstract_excerpt":"We show that for every $d\\ge 1$, if $L_1,\\ldots, L_d$ are linearly ordered compact spaces and there is a continuous surjection \\[ L_1\\times L_2\\times \\dots\\times L_d\\to K_1\\times K_2\\times\\ldots\\times K_{d}\\times K_{d+1},\\] where all the spaces $K_i$ are infinite, then $K_i, K_j$ are metrizable for some $1\\le i<j\\le d+1$. This answers a problem posed by S. Marde\\v{s}i\\'c.\n  We present some related results on Boolean algebras not containing free products with too many uncountable factors. In particular, we answer a problem on initial chain algebras that was posed by L. Baur and L. Heindorf."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10395","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"}