Was the region R meant to be restricted to a single continuous area without holes (i.e. topologically a solid circle but maybe extending to infinity) ? On 29 May 2014, at 20:17, Warren D Smith wrote:
Lunnon: Given a plane curve C defined by f = 0 with f(x, y) polynomial, and a region R of the plane (possibly extending to infinity), I assert that C avoids R provided C avoids the boundary of R ; and C has no critical points within R .
There must be a well-known theorem to this effect (unless, of course, it's actually false...
WDS: a counterexample: C=unit circle, R = thickened version of unit circle (annulus).
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