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

Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54C25, 57N35

Retrieve articles in all journals with MSC: 54C25, 57N35

Additional Information

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