  Using handlebodies we verify a conjecture of P Adjamagbo that if the frontier
of a relatively compact subset $V_0$ of a manifold is a submanifold then there
is an increasing family $\{V_r\}$ of relatively compact open sets indexed by
the positive reals so that the frontier of each is a submanifold, their union
is the whole manifold and for each $r\ge 0$ the subfamily indexed by
$(r,\infty)$ is a neighbourhood basis of the closure of the $r^{\rm th}$ set.
