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

 

Functions not constant on fractal quasi-arcs of critical points


Author: Alec Norton
Journal: Proc. Amer. Math. Soc. 106 (1989), 397-405
MSC: Primary 28A75; Secondary 26B35, 58C25
MathSciNet review: 969524
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Abstract: This paper provides geometric sufficient conditions for an arc to be a critical set for some function not constant along that arc--an example of which was first discovered by Whitney in 1935. In particular, any fractal subarc of a quasi-circle has this property. The maximum degree of differentiability of the function is closely connected to the arc's geometry.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0969524-8
PII: S 0002-9939(1989)0969524-8
Article copyright: © Copyright 1989 American Mathematical Society