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

 

Ambiently universal sets in $ E\sp{n}$


Author: David G. Wright
Journal: Trans. Amer. Math. Soc. 277 (1983), 655-664
MSC: Primary 54C25; Secondary 57N35
MathSciNet review: 694381
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Abstract: For each closed set $ X$ in $ {E^n}$ of dimension at most $ n - 3$, we show that $ X$ fails to be ambiently universal with respect to Cantor sets in $ {E^n}$; i.e., we find a Cantor set $ Y$ in $ {E^n}$ so that for any self-homeomorphism $ h$ of $ {E^n}$, $ h(Y)$ is not contained in $ X$. This result answers a question posed by H. G. Bothe and completes the understanding of ambiently universal sets in $ {E^n}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0694381-6
PII: S 0002-9947(1983)0694381-6
Keywords: Ambiently universal set, ambient embedding, Cantor set, $ n$-dimensional Euclidean space
Article copyright: © Copyright 1983 American Mathematical Society