{"paper":{"title":"On closed embeddings of free topological algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"O.Hryniv, T.Banakh","submitted_at":"2012-02-20T21:59:39Z","abstract_excerpt":"Let $\\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\\mathcal E$ (which means that $\\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all completely regular topological $\\mathcal E$-algebras algebraically isomorphic to members of $\\mathcal K$). For a topological space $X$ by $F(X)$ we denote the free universal $\\mathcal E$-algebra over $X$ in the class $\\mathcal K$. Using some extension properties of the Hartman-Mycielski construction we prove that for a closed subspace $X$ of a metrizable (more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4480","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"}