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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $2$.
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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