{"paper":{"title":"Pseudocompactness, products and topological Brandt $\\lambda^0$-extensions of semitopological monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Oleg Gutik, Oleksandr Ravsky","submitted_at":"2015-10-17T08:15:20Z","abstract_excerpt":"In the paper we study the preservation of pseudocompactness (resp., countable compactness, sequential compactness, $\\omega$-boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff products of pseudocompact (and countably compact) to\\-pological Brandt $\\lambda_i^0$-extensions of semitopological monoids with zero. In particular we show that if $\\big\\{ \\big(B^0_{\\lambda_i}(S_i),\\tau^0_{B(S_i)}\\big) \\colon i\\in\\mathscr{I}\\big\\}$ is a family of Hausdorff pseudocompact to\\-pological Brandt $\\lambda_i^0$-extensions of pseudocompact semitopologi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05096","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"}