Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54F45, 55M10, 54B35

Retrieve articles in all journals with MSC (1991): 54F45, 55M10, 54B35


Additional Information

Leonard R. Rubin
Affiliation: Department of Mathematics, University of Oklahoma, 601 Elm Ave., Rm. 423, Norman, Oklahoma 73019
Email: LRUBIN@ou.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04141-5
PII: S 0002-9939(97)04141-5
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