{"paper":{"title":"The Hausdorff topology as a moduli space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Karan, W. D. Gillam","submitted_at":"2016-01-11T12:50:41Z","abstract_excerpt":"In 1914, F. Hausdorff defined a metric on the set of closed subsets of a metric space $X$. This metric induces a topology on the set $H$ of compact subsets of $X$, called the Hausdorff topology. We show that the topological space $H$ represents the functor on the category of sequential topological spaces taking $T$ to the set of closed subspaces $Z$ of $T \\times X$ for which the projection $\\pi_1 : Z \\to T$ is open and proper. In particular, the Hausdorff topology on $H$ depends on the metric space $X$ only through the underlying topological space of $X$. The Hausdorff space $H$ provides an an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02425","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"}