2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74063Almost 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.Algebraic TopologyGeometric Topology55R19; 55N65text