Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterisation of punctured open $3$-cells
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by O. L. Costich, P. H. Doyle and D. E. Galewski
Proc. Amer. Math. Soc. 28 (1971), 295-298
DOI: https://doi.org/10.1090/S0002-9939-1971-0271919-1

Abstract:

A proof is given using standard methods of the topology of three-dimensional manifolds of the following characterization of punctured cubes: A connected, open $3$-manifold $M$ is topological ${E^3}$ with $k$ points removed if and only if every polyhedral simple closed curve in $M$ lies in a topological cube in $M$ and the rank of ${\pi _2}(M)$ is $k$. An application is given.
References
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Bibliographic Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 295-298
  • MSC: Primary 54.78
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0271919-1
  • MathSciNet review: 0271919