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A new proof of Brown's collaring theorem

1971
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Proceedings of the American Mathematical Society
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The aim of this note is to give a new proof that if a subspace B, compact for convenience, is locally collared in a space X, then it is collared. The idea of the proof is simply to add a collar BXI to X to get X+ and then to construct a homeomorphism of X with X+ by pushing B down on one collared open set at a time. The theorem, of course, is essentially that of [l]. However, the proof easily works in the piecewise linear (PL) category (i.e. all maps are PL and spaces are polyhedra), and when

doi:10.1090/s0002-9939-1971-0267588-7
fatcat:pdegev2e2na53hmlfjg3v4qb6a