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Proceedings of the American Mathematical Society

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

 
 

 

The intersection multiplicity of compact $ n$-dimensional metric spaces


Author: Glenn P. Weller
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
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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}$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0307194-X
Keywords: Metric space, open cover, intersection multiplicity
Article copyright: © Copyright 1972 American Mathematical Society

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