2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65088We present a new direct proof of a topological representation theorem for oriented matroids in the general rank case. Our proof is based on an earlier rank 3 version. It uses hyperline sequences and the generalized Sch{ö}nflies theorem. As an application, we show that one can read off oriented matroids from arrangements of embedded spheres of codimension one, even if wild spheres are involved.21 pages, 4 figuresCombinatoricsGeometric Topology52C40 (Primary) 57N50, 57N45 (Secondary)text