Sticky arcs in

Author:
David G. Wright

Journal:
Proc. Amer. Math. Soc. **66** (1977), 181-182

MSC:
Primary 57A15; Secondary 55A35

MathSciNet review:
0515648

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let *A* and *B* be arcs in , Euclidean 3-space. Then *A* can be ``slipped'' off *B*; i.e., there exists a homeomorphism of onto itself, arbitrarily close to the identity, such that . The purpose of this note is to show that arcs in do not always enjoy this property. The examples depend heavily on a recent result of McMillan.

**[1]**Steve Armentrout,*Decompostions of 𝐸³ with a compact 𝑂-dimensional set of nondegenerate elements*, Trans. Amer. Math. Soc.**123**(1966), 165–177. MR**0195074**, 10.1090/S0002-9947-1966-0195074-4**[2]**Morton Brown,*A proof of the generalized Schoenflies theorem*, Bull. Amer. Math. Soc.**66**(1960), 74–76. MR**0117695**, 10.1090/S0002-9904-1960-10400-4**[3]**Robert D. Edwards and Robion C. Kirby,*Deformations of spaces of imbeddings*, Ann. Math. (2)**93**(1971), 63–88. MR**0283802****[4]**D. R. McMillan Jr.,*An arc in a 𝑃𝐿 𝑛-manifold with no neighborhood that embeds in 𝑆ⁿ,𝑛≥4*, Michigan Math. J.**25**(1978), no. 1, 29–43. MR**0482772****[5]**D. R. McMillan Jr.,*A criterion for cellularity in a manifold. II*, Trans. Amer. Math. Soc.**126**(1967), 217–224. MR**0208583**, 10.1090/S0002-9947-1967-0208583-7**[6]**C. L. Seebeck III,*Collaring and (𝑛-1)-manifold in an 𝑛-manifold*, Trans. Amer. Math. Soc.**148**(1970), 63–68. MR**0258045**, 10.1090/S0002-9947-1970-0258045-6

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
57A15,
55A35

Retrieve articles in all journals with MSC: 57A15, 55A35

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1977-0515648-0

Article copyright:
© Copyright 1977
American Mathematical Society