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Cohomological dimension and approximate limits

Author: Leonard R. Rubin
Journal: Proc. Amer. Math. Soc. 125 (1997), 3125-3128
MSC (1991): Primary 54F45, 55M10, 54B35
MathSciNet review: 1423333
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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 $\dim _{G} X\leq n$.

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Additional Information

Leonard R. Rubin
Affiliation: Department of Mathematics, University of Oklahoma, 601 Elm Ave., Rm. 423, Norman, Oklahoma 73019

Keywords: Dimension, cohomological dimension, Eilenberg-Mac\, Lane complex, approximate (inverse) system, inverse system, resolution, approximate resolution
Received by editor(s): November 16, 1995
Communicated by: James West
Article copyright: © Copyright 1997 American Mathematical Society

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