  The 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.
