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

Sticky arcs in $ E\sp{n}$ $ (n\geq 4)$


Author: David G. Wright
Journal: Proc. Amer. Math. Soc. 66 (1977), 181-182
MSC: Primary 57A15; Secondary 55A35
MathSciNet review: 0515648
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Abstract: Let A and B be arcs in $ {E^3}$, Euclidean 3-space. Then A can be ``slipped'' off B; i.e., there exists a homeomorphism of $ {E^3}$ onto itself, arbitrarily close to the identity, such that $ h(A) \cap B = \emptyset $. The purpose of this note is to show that arcs in $ {E^n}(n \geqslant 4)$ do not always enjoy this property. The examples depend heavily on a recent result of McMillan.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0515648-0
PII: S 0002-9939(1977)0515648-0
Article copyright: © Copyright 1977 American Mathematical Society