{"paper":{"title":"$F$-Dugundji spaces, $F$-Milutin spaces and absolute $F$-valued retracts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Taras Banakh, Taras Radul","submitted_at":"2014-01-10T13:03:27Z","abstract_excerpt":"For every functional functor $F:Comp\\to Comp$ in the category $Comp$ of compact Hausdorff spaces we define the notions of $F$-Dugundji and $F$-Milutin spaces, generalizing the classical notions of a Dugundji and Milutin spaces. We prove that the class of $F$-Dugundji spaces coincides with the class of absolute $F$-valued retracts. Next, we show that for a monomorphic continuous functor $F:Comp\\to Comp$ admitting tensor products each Dugundji compact is an absolute $F$-valued retract if and only if the doubleton $\\{0,1\\}$ is an absolute $F$-valued retract if and only if some points $a\\in F(\\{0\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2319","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"}