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Relative collaring


Author: Leonard R. Rubin
Journal: Proc. Amer. Math. Soc. 55 (1976), 181-184
MSC: Primary 57A40
DOI: https://doi.org/10.1090/S0002-9939-1976-0410755-4
MathSciNet review: 0410755
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Abstract: It was proved by Morton Brown that the boundary of a manifold has a collar neighborhood. Later Robert Connelly gave a different proof of that result, and his method of proof was used by T. Benny Rushing to prove a relative collaring theorem. This paper contains a relative collaring theorem that is more general than either of the two just mentioned.


References [Enhancements On Off] (What's this?)

  • [Co] Robert Connelly, A new proof of Brown's collaring theorem, Proc. Amer. Math. Soc. 27 (1971), 180-182. MR 42 #2490. MR 0267588 (42:2490)
  • [Da] Jerome Dancis, Shrinking collapsible sets in topological manifolds and embedding manifolds ``rel'' the boundary, University of Maryland Technical Report TR 74-49, 1974, 25 pp.
  • [Du] James Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
  • [Mi] E. A. Michael, Local properties of topological spaces, Duke Math. J. 21 (1954), 163-171. MR 15, 977. MR 0062424 (15:977c)
  • [Ru] T. Benny Rushing, Topological embeddings, Academic Press, New York and London, 1973. MR 0348752 (50:1247)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0410755-4
Keywords: Locally collared, closed collar
Article copyright: © Copyright 1976 American Mathematical Society

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