{"paper":{"title":"Extended-valued topical and anti-topical functions on semimodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.OC","authors_text":"Ivan Singer, Viorel Nitica","submitted_at":"2012-12-28T20:31:16Z","abstract_excerpt":"In previous papers we have studied topical functions f:X-> K and related classes of functions, where X is a b-complete semimodule over an idempotent b-complete semifield K. Without essential restriction of the generality, we assume that K has no greatest element sup K, and hence for x in X and y=inf X the residuation x/y is not defined. Now we adjoin to K an outside \"greatest element\" top =sup K, and extending in a suitable way the operations of multiplication and addition from K to bar K, which is the union of K and top, we study \"extended functions\" f:X-> bar K. Actually, we give two differe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6561","kind":"arxiv","version":4},"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"}