## Cohomological dimension and approximate limits

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- by Leonard R. Rubin
- Proc. Amer. Math. Soc.
**125**(1997), 3125-3128 - DOI: https://doi.org/10.1090/S0002-9939-97-04141-5
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## Abstract:

Approximate (inverse) systems of compacta have been useful in the study of covering dimension, dim, and cohomological dimension over an abelian group $G$, $\dim _{G}$. Such systems are more general than (classical) inverse systems. They have limits and structurally have similar properties. In particular, the limit of an approximate system of compacta satisfies the important property of being an approximate resolution. We shall prove herein that if $G$ is an abelian group, a compactum $X$ is the limit of an approximate system of compacta $X_{a}$, $n\in \mathbb {N}$, and $\dim _{G} X_{a}\leq n$ for each $a$, then $\dim _{G} X\leq n$.## References

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## Bibliographic Information

**Leonard R. Rubin**- Affiliation: Department of Mathematics, University of Oklahoma, 601 Elm Ave., Rm. 423, Norman, Oklahoma 73019
- Email: LRUBIN@ou.edu
- Received by editor(s): November 16, 1995
- Communicated by: James West
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 3125-3128 - MSC (1991): Primary 54F45, 55M10, 54B35
- DOI: https://doi.org/10.1090/S0002-9939-97-04141-5
- MathSciNet review: 1423333