Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • [1] J. F. P. Hudson, Piecewise linear topology, Benjamin, New York, 1969. MR 40 #2094. MR 0248844 (40:2094)
  • [2] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961. MR 23 #A2857. MR 0125557 (23:A2857)
  • [3] Y. Shikata, On the smoothing problem and the size of a topological manifold, Osaka J. Math. 3 (1966), 293-301. MR 35 #6148. MR 0215307 (35:6148)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E35

Retrieve articles in all journals with MSC: 54E35


Additional Information

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

American Mathematical Society