Abstract. We p r o ve t h a t i f X is a locally nite n-dimensional polyhedron such that X Q admits a Z-compacti cation, then X I 2n+5 also admits a Z-compacti cation. Our argument relies on an extension of Dierker's Lemma 6], 2] which s a ys that if P p and Q q are locally nite polyhedra, p 3 a n d c : P ! Q is a PL surjection with contractible pointinverses, then Q I 2p+1 collapses to P . See Proposition 1.5 for details, including control on the collapse. In the last section, we g i v e an example of a unif…
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