{"paper":{"title":"On the Menger covering property and $D$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Du\\v{s}an Repov\\v{s}, Lyubomyr Zdomskyy","submitted_at":"2010-12-06T08:44:58Z","abstract_excerpt":"The main results of this note are: It is consistent that every subparacompact space $X$ of size $\\omega_1$ is a $D$-space; If there exists a Michael space, then all productively Lindel\\\"of spaces have the Menger property, and, therefore, are $D$-spaces; and\n  Every locally $D$-space which admits a $\\sigma$-locally finite cover by Lindel\\\"of spaces is a $D$-space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1094","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"}