{"paper":{"title":"Cofinite subsets and double negation topologies on locales of filters and ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Jos\\'e Manuel Garc\\'ia-Calcines, Luis Espa\\~nol, M. Carmen M\\'inguez","submitted_at":"2015-03-18T18:53:11Z","abstract_excerpt":"We study the role of the filter $c\\mathcal{K}(X)$ of cofinite subsets of $X$ in the locale $\\mathcal{F}ilt(X)$ of all filters on $X$, by means of the double negation topology of $\\mathcal{F}ilt(X)$, and an essential locale morphism $\\mathcal{P}(X)^{op}\\to\\mathcal{F}ilt(X)$. Moreover, in the case $X=\\mathbb{N}$, we characterise cofinite subsets by means of the double negation topology on the monoid $\\mathbb{M}$ of the maps $\\mathbb{N}\\to \\mathbb{N}$ with finite fibers, or on the submonoid $\\mathbb{E}\\subseteq \\mathbb{M}$ of the monotone and injective maps $\\mathbb{N}\\to\\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05531","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"}