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Isotopy and homeomorphism


Author: Dennis Kibler
Journal: Proc. Amer. Math. Soc. 26 (1970), 499-502
MSC: Primary 54.28; Secondary 55.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0266148-0
MathSciNet review: 0266148
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Abstract: If $ X$ and $ Y$ are isotopically equivalent topological spaces, they are not necessarily homeomorphic. If $ X$ and $ Y$ are compact without boundary manifolds or $ n$-pure simplicial complexes, then isotopy equivalence implies topological equivalence. An example of compact manifolds with boundaries which are not homeomorphic but are isotopically equivalent is given.


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

  • [1] D. H. Gottlieb, Homotopy and isotopy properties of topological spaces, Canad. J. Math. 16 (1964), 561-571. MR 29 #614. MR 0163311 (29:614)
  • [2] S. T. Hu, Homotopy and isotopy properties of topological spaces, Canad. J. Math. 13 (1961), 167-176. MR 25 #574 MR 0137118 (25:574)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0266148-0
Keywords: Isotopy equivalence, $ n$-pure simplicial complex, stringless simplicial complex
Article copyright: © Copyright 1970 American Mathematical Society

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