{"paper":{"title":"$\\aleph$-injective Banach spaces and $\\aleph$-projective compacta","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, F\\'elix Cabello S\\'anchez, Jes\\'us M. F. Castillo, Manuel Gonz\\'alez, Yolanda Moreno","submitted_at":"2014-06-25T23:29:08Z","abstract_excerpt":"A Banach space $E$ is said to be injective if for every Banach space $X$ and every subspace $Y$ of $X$ every operator $t:Y\\to E$ has an extension $T:X\\to E$. We say that $E$ is $\\aleph$-injective (respectively, universally $\\aleph$-injective) if the preceding condition holds for Banach spaces $X$ (respectively $Y$) with density less than a given uncountable cardinal $\\aleph$. We perform a study of $\\aleph$-injective and universally $\\aleph$-injective Banach spaces which extends the basic case where $\\aleph=\\aleph_1$ is the first uncountable cardinal. When dealing with the corresponding \"isomet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6733","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"}