{"paper":{"title":"Covering locally compact groups by less than $2^\\om$ many translates of a compact nullset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"\\'Arp\\'ad T\\'oth, M\\'arton Elekes","submitted_at":"2011-09-24T21:03:20Z","abstract_excerpt":"Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr\\=ans gave an affirmative answer by showing that if $C_{EK}$ is the well known compact nullset considered first by Erd\\H os and Kakutani then $\\RR$ can be covered by $\\cof(\\iN)$ many translates of $C_{EK}$. As this set has no analogue in more general groups, it was posed as an open question whether such a result holds for uncountable locally compact Polish groups. In this paper we give an affirmat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5308","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"}