2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154310The totally nonnegative part of a partial flag variety G/P has been shown by the first author to be a union of semi-algebraic cells. Moreover she showed that the closure of a cell is the union of smaller cells. In this note we provide glueing maps for each of the cells to prove that the totally nonnegative part of G/P is a CW complex. This generalizes a result of Postnikov, Speyer and the second author for Grassmannians.14 pagesAlgebraic Geometry14m15; 20G15text