  For each composite number $n\ne 2^k$, there does not exist a single connected
closed $(n+1)$-manifold such that any smooth, simply-connected, closed
$n$-manifold can be topologically flat embedded into it. There is a single
connected closed 5-manifold $W$ such that any simply-connected, 4-manifold $M$
can be topologically flat embedded into $W$ if $M$ is either closed and
indefinite, or compact and with non-empty boundary.
