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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Property C, refinable maps and dimension raising maps


Authors: Dennis J. Garity and Dale M. Rohm
Journal: Proc. Amer. Math. Soc. 98 (1986), 336-340
MSC: Primary 54F45; Secondary 54C10
MathSciNet review: 854043
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Abstract: We show that refinable maps defined on compacta preserve Property C. H. Kato has proved the analogous result for weakly infinite dimensional spaces. We also show that if $ f$ is a map from a compact $ C$ space $ X$ onto a non $ C$ space $ Y$, then the set of points in $ Y$ with an uncountable number of preimages is a space that does not have Property C.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854043-7
PII: S 0002-9939(1986)0854043-7
Keywords: Property C, refinable map, countable dimensional, weakly infinite dimensional
Article copyright: © Copyright 1986 American Mathematical Society