{"paper":{"title":"Homogeneity degree of some symmetric products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Rodrigo Hern\\'andez-Guti\\'errez, Ver\\'onica Mart\\'inez-de-la-Vega","submitted_at":"2016-06-03T17:18:11Z","abstract_excerpt":"For a metric continuum $X$, we consider the $n^{\\tiny\\textrm{th}}$-symmetric product $F_{n}(X)$ defined as the hyperspace of all nonempty subsets of $X$ with at most $n$ points. The homogeneity degree $hd(X)$ of a continuum $X$ is the number of orbits for the action of the group of homeomorphisms of $X$ onto itself. In this paper we determine $hd(F_{n}(X))$ for every manifold without boundary and $n\\in \\mathbb{N}$. We also compute $hd(F_{n}[0,1])$ for all $n\\in \\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01193","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"}