2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102236The totally nonnegative part of a partial flag variety G/P is known to have a decomposition into semi-algebraic cells. We show that the closure of a cell is again a union of cells and give a combinatorial description of the closure relations. The totally nonnegative cells are defined by intersecting the totally nonnegative part with a certain stratification of G/P defined by Lusztig. We also verify the same closure relations for these strata.12 pages, 1 figure, improved referencesAlgebraic Geometrytext