{"paper":{"title":"Selection type results and fixed point property for affine bi-Lipschitz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cleon S. Barroso, Torrey M. Gallagher","submitted_at":"2019-02-28T00:46:58Z","abstract_excerpt":"We obtain a refinement of a selection principle for $(\\mathcal{K}, \\lambda)$-wide-$(s)$ sequences in Banach spaces due to Rosenthal. This result is then used to show that if $C$ is a bounded, non-weakly compact, closed convex subset of a Banach space $X$, then there exists a Hausdorff vector topology $\\tau$ on $X$ which is weaker than the weak topology, a closed, convex $\\tau$-compact subset $K$ of $C$ and an affine bi-Lipschitz map $T: K\\to K$ without fixed points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10852","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"}