A one dimensional manifold is of cohomological dimension $2$
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- by Satya Deo PDF
- Proc. Amer. Math. Soc. 52 (1975), 445-446 Request permission
Abstract:
G. Bredon defines the cohomological Dimension of a topological space $X$ to be the supremum of all cohomological $\phi$-dimensions of $X$, where $\phi$ varies over the entire families of supports on $X$. He has proved that if $X$ is a topological $n$-manifold then the cohomological Dimension of $X$ is $n$ or $n + 1$. He was not able to decide which one it is, even for a space as simple as the real line. The objective of this paper is to solve his problem for $n = 1$. In particular, we have shown that the cohomological Dimension of the real line is $2$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 445-446
- MSC: Primary 55B30; Secondary 57A65
- DOI: https://doi.org/10.1090/S0002-9939-1975-0394632-2
- MathSciNet review: 0394632