  We show that if a non-degenerate PL map $f:N\to M$ lifts to a topological
embedding in $M\times\mathbb R^k$ then it lifts to a PL embedding in there. We
also show that if a stable smooth map $N^n\to M^m$, $m\ge n$, lifts to a
topological embedding in $M\times\mathbb R$, then it lifts to a smooth
embedding in there.
