{"paper":{"title":"Representation of group isomorphisms. The compact case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Margarita Gary, Mar\\'ia V. Ferrer, Salvador Hern\\'andez","submitted_at":"2014-11-06T13:00:26Z","abstract_excerpt":"Let $G$ be a discrete group and let $\\mathcal A$ and $\\mathcal B$ be two subgroups of $G$-valued continuous functions defined on two $0$-dimensional compact spaces $X$ and $Y$. A group isomorphism $H$ defined between $\\mathcal A$ and $\\mathcal B$ is called \\textit{separating} when for each pair of maps $f,g\\in \\mathcal A$ satisfying that $f^{-1}(e_G)\\cup g^{-1}(e_G)=X$, it holds that $Hf^{-1}(e_G)\\cup Hg^{-1}(e_G)=Y$. We prove that under some mild conditions every separating isomorphism $H:\\mathcal A\\longrightarrow \\mathcal B$ can be represented by means of a continuous function $h: Y\\longrigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1593","kind":"arxiv","version":2},"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"}