{"paper":{"title":"An example of a rigid $\\kappa$-superuniversal metric space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Wojciech Bielas","submitted_at":"2014-07-14T18:58:43Z","abstract_excerpt":"For a cardinal $\\kappa > \\omega$ a metric space $X$ is called to be $\\kappa$-superuniversal whenever for every metric space $Y$ with $|Y| < \\kappa$ every partial isometry from a subset of $Y$ into $X$ can be extended over the whole space $Y$. Examples of such spaces were given by Hechler [1] and Kat\\v{e}tov [2]. In particular, Kat\\v{e}tov showed that if $\\omega < \\kappa = \\kappa^{< \\kappa}$, then there exists a $\\kappa$-superuniversal $K$ which is moreover $\\kappa$-homogeneous, i.e. every isometry of a subspace $Y\\subseteq K$ with $|Y|<\\kappa$ can be extended to an isometry of the whole $K$. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3767","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"}