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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On pairs of nonintersecting faces of cell complexes
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by Philip L. Wadler PDF
Proc. Amer. Math. Soc. 51 (1975), 438-440 Request permission

Abstract:

We show that, for all cell complexes whose underlying set is a manifold, $M$, an alternating sum of numbers of pairs of faces that do not intersect is a topological invariant. This is done by proving that it is a function of the Euler characteristic, $x$, of $M$.
References
    B. Grünbaum, Convex polytopes, Pure and Appl. Math., vol. 16, Interscience, New York, 1967. MR 37 #2085.
  • Wu Wen-tsün, A theory of imbedding, immersion, and isotopy of polytopes in a euclidean space, Science Press, Peking, 1965. MR 0215305
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 438-440
  • MSC: Primary 57C05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0400241-9
  • MathSciNet review: 0400241