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ANALYTIC NON-BOREL SETS AND VERTICES OF DIFFERENTIABLE CURVES IN THE PLANE

ANALYTIC NON-BOREL SETS AND VERTICES OF DIFFERENTIABLE CURVES IN THE PLANE

The purpose of this paper is to show that given any non-zero cardinal number $n \leq {\aleph }_{0}$, the set of differentiable paths of class $C^{2}$ and of unit length in the plane having their arc length as the parameter in $[0,1]$ and tracing curves which have at least $n$ …