{"paper":{"title":"A Universal Continuum of Weight aleph","license":"","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Alan Dow, Klaas Pieter Hart","submitted_at":"1998-05-04T08:39:17Z","abstract_excerpt":"We prove that every continuum of weight aleph_1 is a continuous image of the Cech-Stone-remainder R^* of the real line. It follows that under CH the remainder of the half line [0,infty) is universal among the continua of weight c --- universal in the `mapping onto' sense.\n  We complement this result by showing that\n 1) under MA every continuum of weight less than c is a continuous image of R^*\n 2) in the Cohen model the long segment of length omega_2+1 is not a continuous image of R^*, and\n 3) PFA implies that I_u is not a continuous image of R^*, whenever u is a c-saturated ultrafilter. We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9805008","kind":"arxiv","version":3},"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"}