{"paper":{"title":"Fundamental bounded resolutions and quasi-$(DF)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"J.C. Ferrando, J. K\\c{a}kol, S. Gabriyelyan","submitted_at":"2017-11-12T18:39:57Z","abstract_excerpt":"We introduce a new class of locally convex spaces $E$, under the name quasi-$(DF)$-spaces, containing strictly the class of $(DF)$-spaces. A locally convex space $E$ is called a quasi-$(DF)$-space if (i) $E$ admits a fundamental bounded resolution, i.e. an $\\mathbb{N}^{\\mathbb{N}}$-increasing family of bounded sets in $E$ which swallows all bounded set in $E$, and (ii) $E$ belongs to the class $\\mathfrak{G}$ (in sense of Cascales--Orihuela). The class of quasi-$(DF)$-spaces is closed under taking subspaces, countable direct sums and countable products. Every regular $(LM)$-space (particularly,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04336","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"}