{"paper":{"title":"Hyperspaces of countable compacta","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Krzysztof Omiljanowski, Pawe{\\l} Krupski, Taras Banakh","submitted_at":"2019-08-07T21:23:58Z","abstract_excerpt":"Hyperspaces $\\mathcal H(X)$ of all countable compact subsets of a metric space $X$ and $\\mathcal A_n(X)$ of infinite compact subsets which have at most $n$ ($n\\in\\mathbb N$), or finitely many ($n=\\omega$) or countably many ($n=\\omega+1$) accumulation points are studied. By descriptive set-theoretical methods, we fully characterize them for 0-dimensional, dense-in-itself, Polish spaces and partially for $\\sigma$-compact spaces $X$. Using the theory of absorbing sets, we get characterizations of $\\mathcal H(X)$, $\\mathcal A_\\omega(X)$ and $\\mathcal A_{\\omega+1}(X)$ for nondegenerate connected, l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02845","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02845/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}