{"paper":{"title":"On the remainder of the semialgebraic Stone-C\\v{e}ch compactification of a semialgebraic set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J.M. Gamboa, Jos\\'e F. Fernando","submitted_at":"2015-03-25T22:25:35Z","abstract_excerpt":"In this work we analyze some topological properties of the remainder $\\partial M:=\\beta_s^* M\\setminus M$ of the semialgebraic Stone-C\\v{e}ch compactification $\\beta_s^* M$ of a semialgebraic set $M\\subset{\\mathbb R}^m$ in order to `distinguish' its points from those of $M$. To that end we prove that the set of points of $\\beta_s^* M$ that admit a metrizable neighborhood in $\\beta_s^* M$ equals $M_{\\rm lc}\\cup( {\\rm Cl}_{\\beta_s^* M}(\\overline{M}_{\\leq1})\\setminus\\overline{M}_{\\leq1})$ where $M_{\\rm lc}$ is the largest locally compact dense subset of $M$ and $\\overline{M}_{\\leq1}$ is the closu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07567","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"}