{"paper":{"title":"The topology of systems of hyperspaces determined by dimension functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GN","authors_text":"N.Mazurenko, T.Banakh","submitted_at":"2009-08-16T10:11:38Z","abstract_excerpt":"Given a non-degenerate Peano continuum $X$, a dimension function $D:2^X_*\\to[0,\\infty]$ defined on the family $2^X_*$ of compact subsets of $X$, and a subset $\\Gamma\\subset[0,\\infty)$, we recognize the topological structure of the system $(2^X,\\D_{\\le\\gamma}(X))_{\\alpha\\in\\Gamma}$, where $2^X$ is the hyperspace of non-empty compact subsets of $X$ and $D_{\\le\\gamma}(X)$ is the subspace of $2^X$, consisting of non-empty compact subsets $K\\subset X$ with $D(K)\\le\\gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2229","kind":"arxiv","version":5},"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"}