{"paper":{"title":"Lattice isomorphisms between certain sublattices of continuous functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fereshteh Sady, Vahid Ehsani","submitted_at":"2019-07-20T09:39:12Z","abstract_excerpt":"Let $C(X,I)$ be the lattice of all continuous functions on a compact Hausdorff space $X$ with values in the unit interval $I=[0,1]$. We show that for compact Hausdorff spaces $X$ and $Y$ and (not necessarily contain constants) sublattices $A$ and $B$ of $C(X,I)$ and $C(Y,I)$, respectively, which satisfy a certain separation property, any lattice isomorphism $\\varphi : A \\longrightarrow B$ induces a homeomorphism $\\mu: Y \\longrightarrow X$. If, furthermore, $A$ and $B$ are closed under the multiplication, then $\\varphi$ has a representation $\\varphi(f)(y)=m_y(f(\\mu(y)))$, $f\\in A$, for all poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08786","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"}