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The intersection multiplicity of $ n$-dimensional paracompact spaces

Author: Glenn P. Weller
Journal: Proc. Amer. Math. Soc. 50 (1975), 402-404
MSC: Primary 54D20
MathSciNet review: 0372822
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Abstract: It is shown that there is an integer $ \nu (n) \leq {3^{2n + 1}} - 1$ such that any $ n$-dimensional paracompact space $ X$ has intersection multiplicity at most $ \nu (n)$. That is, if $ \mathcal{U}$ is an open cover of $ X$, then there is an open cover $ \mathcal{V}$ refining $ \mathcal{U}$ such that any element of $ \mathcal{V}$ intersects at most $ \nu (n)$ elements of $ \mathcal{V}$.

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

  • [1] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961. MR 23 #A2857. MR 0125557 (23:A2857)
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Keywords: Intersection multiplicity, paracompact spaces, simplicial complex, dimension
Article copyright: © Copyright 1975 American Mathematical Society

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