Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Metrizable spaces where the inductive dimensions disagree


Author: John Kulesza
Journal: Trans. Amer. Math. Soc. 318 (1990), 763-781
MSC: Primary 54F45
MathSciNet review: 954600
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A method for constructing zero-dimensional metrizable spaces is given. Using generalizations of Roy's technique, these spaces can often be shown to have positive large inductive dimension. Examples of $ {\mathbf{N}}$-compact, complete metrizable spaces with $ \operatorname{ind} = 0$ and $ \operatorname{Ind} = 1$ are provided, answering questions of Mrowka and Roy. An example with weight $ \mathfrak{c}$ and positive Ind such that subspaces with smaller weight have $ \operatorname{Ind} = 0$ is produced in ZFC. Assuming an additional axiom, for each cardinal $ \lambda $ a space of positive Ind with all subspaces with weight less than $ \lambda $ strongly zero-dimensional is constructed.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54F45

Retrieve articles in all journals with MSC: 54F45


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0954600-9
PII: S 0002-9947(1990)0954600-9
Keywords: Metrizable space, full set, dimension
Article copyright: © Copyright 1990 American Mathematical Society