{"paper":{"title":"Topological groups, \\mu-types and their stabilizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Sergei Starchenko, Ya'acov Peterzil","submitted_at":"2014-09-18T16:04:29Z","abstract_excerpt":"We consider an arbitrary topological group $G$ definable in a structure $\\mathcal M$, such that some basis for the topology of $G$ consists of sets definable in $\\mathcal M$.\n  To each such group $G$ we associate a compact $G$-space of partial types $S^\\mu_G(M)=\\{p_\\mu:p\\in S_G(M)\\}$ which is the quotient of the usual type space $S_G(M)$ by the relation of two types being \"infinitesimally close to each other\". In the o-minimal setting, if $p$ is a definable type then it has a corresponding definable subgroup $Stab_\\mu(p)$, which is the stabilizer of $p_\\mu$. This group is nontrivial when $p$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5355","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"}