{"paper":{"title":"Geometrical characterization of semilinear isomorphisms of vector spaces and semilinear homeomorphisms of normed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.RT","authors_text":"Mark Pankov","submitted_at":"2013-04-05T07:16:21Z","abstract_excerpt":"Let $V$ and $V'$ be vector spaces over division rings (possible infinite-dimensional) and let ${\\mathcal P}(V)$ and ${\\mathcal P}(V')$ be the associated projective spaces. We say that $f:{\\mathcal P}(V)\\to {\\mathcal P}(V')$ is a PGL-{\\it mapping} if for every $h\\in {\\rm PGL}(V)$ there exists $h'\\in {\\rm PGL}(V')$ such that $fh=h'f$. We show that for every PGL-bijection the inverse mapping is a semicollineation. Also, we obtain an analogue of this result for the projective spaces associated to normed spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1626","kind":"arxiv","version":2},"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"}