The intersection multiplicity of $n$-dimensional paracompact spaces
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- by Glenn P. Weller PDF
- Proc. Amer. Math. Soc. 50 (1975), 402-404 Request permission
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
- John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
- Glenn P. Weller, The intersection multiplicity of compact $n$-dimensional metric spaces, Proc. Amer. Math. Soc. 36 (1972), 293–294. MR 307194, DOI 10.1090/S0002-9939-1972-0307194-X
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 402-404
- MSC: Primary 54D20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0372822-2
- MathSciNet review: 0372822