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)

 

On the dimension of limits of inverse systems


Author: Yukinobu Yajima
Journal: Proc. Amer. Math. Soc. 91 (1984), 461-466
MSC: Primary 54F45; Secondary 54B10
MathSciNet review: 744649
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We say that the limit of an inverse system $ X = \underleftarrow {\lim }\left\{ {{X_\lambda },\pi _\mu ^\lambda ,\Lambda } \right\}$ is cylindrical if each finite cozero cover of $ X$ has a $ \sigma $-locally finite refinement consisting of sets of the form $ \pi _\lambda ^{ - 1}(U)$, where $ U$ is a cozero-set in $ {X_\lambda }$ and $ {\pi _\lambda }:X \to {X_\lambda }$ is the projection.

We prove that if $ X$ is cylindrical, then $ \dim X = \sup \left\{ {\dim {X_\lambda }:\lambda \in \Lambda } \right\}$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F45, 54B10

Retrieve articles in all journals with MSC: 54F45, 54B10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744649-6
PII: S 0002-9939(1984)0744649-6
Keywords: Covering dimension, limit of inverse system, cylindrical, cozero cylinder, perforable inverse sequence, Cartesian product, finite subproduct
Article copyright: © Copyright 1984 American Mathematical Society