{"paper":{"title":"The new $\\nu$-metric induces the classical gap topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA","math.KT"],"primary_cat":"math.OC","authors_text":"Amol Sasane","submitted_at":"2010-12-02T14:19:29Z","abstract_excerpt":"Let $\\calA_+$ denote the set of Laplace transforms of complex Borel measures $\\mu$ on $[0,+\\infty)$ such that $\\mu$ does not have a singular non-atomic part. In \\cite{BalSas}, an extension of the classical $\\nu$-metric of Vinnicombe was given, which allowed one to address robust stabilization problems for unstable plants over $\\calA_+$. In this article, we show that this new $\\nu$-metric gives a topology on unstable plants which coincides with the classical gap topology for unstable plants over $\\calA_+$ with a single input and a single output."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0427","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"}