{"paper":{"title":"Spaces of Remote Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Angel Tamariz-Mascar\\'ua, Michael Hru\\v{s}\\'ak, Rodrigo Hern\\'andez-Guti\\'errez","submitted_at":"2018-09-18T16:13:09Z","abstract_excerpt":"Given a Tychonoff space $X$, let $\\varrho(X)$ be the set of remote points of $X$. We view $\\varrho(X)$ as a topological space. In this paper we assume that $X$ is metrizable and ask for conditions on $Y$ so that $\\varrho(X)$ is homeomorphic to $\\varrho(Y)$. This question has been studied before by R. G. Woods and C. Gates. We give some results of the following type: if $X$ has topological property $\\mathbf{P}$ and $\\varrho(X)$ is homeomorphic to $\\varrho(Y)$, then $Y$ also has $\\mathbf{P}$. We also characterize the remote points of the rationals and irrationals up to some restrictions. Further"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06813","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"}