  Almost forty years ago, C.T.C. Wall systematically analyzed the set of
"thickenings" of a finite CW complex. Of the results he obtained, probably the
most computationally important is the "suspension theorem," which is an exact
sequence relating the n-dimensional thickenings of a finite complex to its
(n+1)-dimensional ones. The object of this note is to fill in what we believe
is a missing argument in the proof of that theorem.
