{"paper":{"title":"Noetherian Quasi-Polish Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.GN","authors_text":"Arno Pauly, Matthew de Brecht","submitted_at":"2016-07-25T14:28:18Z","abstract_excerpt":"In the presence of suitable power spaces, compactness of $\\mathbf{X}$ can be characterized as the singleton $\\{X\\}$ being open in the space $\\mathcal{O}(\\mathbf{X})$ of open subsets of $\\mathbf{X}$. Equivalently, this means that universal quantification over a compact space preserves open predicates.\n  Using the language of represented spaces, one can make sense of notions such as a $\\Sigma^0_2$-subset of the space of $\\Sigma^0_2$-subsets of a given space. This suggests higher-order analogues to compactness: We can, e.g.~, investigate the spaces $\\mathbf{X}$ where $\\{X\\}$ is a $\\Delta^0_2$-sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07291","kind":"arxiv","version":2},"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"}