  The image of the branch set of a PL branched cover between PL $n$-manifolds
is a simplicial $(n-2)$-complex. We demonstrate that the reverse implication
also holds: an open and discrete map $f \colon \mathbb{S}^n \to \mathbb{S}^n$
with the image of the branch set contained in a simplicial $(n-2)$-complex is
equivalent up to homeomorphism to a PL branched cover.
