The intersection multiplicity of compact $n$-dimensional metric spaces
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- by Glenn P. Weller PDF
- Proc. Amer. Math. Soc. 36 (1972), 293-294 Request permission
Abstract:
It is shown that there is an integer $\mu (n)$ such that any compact n-dimensional metric space M has intersection multiplicity at most $\mu (n)$. That is, if $\mathcal {U}$ is an open cover of M, then there is an open cover $\mathcal {V}$ refining $\mathcal {U}$ such that any element of $\mathcal {V}$ can intersect at most $\mu (n)$ other elements of $\mathcal {V}$.References
- J. F. P. Hudson, Piecewise linear topology, W. A. Benjamin, Inc., New York-Amsterdam, 1969. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees. MR 0248844
- John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
- Yoshihiro Shikata, On the smoothing problem and the size of a topological manifold, Osaka Math. J. 3 (1966), 293–301. MR 215307
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 293-294
- MSC: Primary 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1972-0307194-X
- MathSciNet review: 0307194