{"paper":{"title":"Dual Selection Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Steven Clontz","submitted_at":"2018-09-27T22:19:40Z","abstract_excerpt":"Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger selection game involving open covers is dual to the point-open game. This extends to a general theorem: if $\\{\\operatorname{ran}{f}:f\\in\\mathbf C(\\mathcal R)\\}$ is coinitial in $\\mathcal A$ with respect to $\\subseteq$, where $\\mathbf C(\\mathcal R)=\\{f\\in(\\bigcup\\mathcal R)^{\\mathcal R}:R\\in\\mathcal R\\Rightarrow f(R)\\in R\\}$ collects the choice functions on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10783","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"}