{"paper":{"title":"A class of metrizable locally quasi-convex groups which are not Mackey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dikran Dikranjan, Elena Mart\\'in Peinador, Vaja Tarieladze","submitted_at":"2010-12-28T08:02:00Z","abstract_excerpt":"A topological group $(G,\\mu)$ from a class $\\mathcal G$ of MAP topological abelian groups will be called a {\\it Mackey group} in $\\mathcal G$ if it has the following property: if $\\nu$ is a group topology in $G$ such that $(G,\\nu)\\in \\mathcal G$ and $(G,\\nu)$ has the same continuous characters, say $(G,\\nu)^{\\wedge}=(G,\\mu)^{\\wedge}$, then $\\nu\\le \\mu$.\n  If $\\rm{LCS}$ is the class of Hausdorff topological abelian groups which admit a structure of a locally convex topological vector space over $\\mathbb R$, it is well-known that every metrizable $(G,\\mu) \\in \\rm{LCS}$ is a Mackey group in $\\rm{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5713","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"}