It has a topological dimension of 1, but it is by no means a rectifiable curve : the infinite.
2.
Among the problems Alexander had solved was finding the polynomial hull of rectifiable curves in the space of several complex variables.
3.
In 1902, Hurwitz published a short proof using the Fourier series that applies to arbitrary rectifiable curves ( not assumed to be smooth ).
4.
In geometric measure theory such a smooth curve as the circle that can be approximated by small straight segments with a definite limit is termed a rectifiable curve.
5.
By using the Cauchy integral theorem, one can show that the integral over " C " ( or the closed rectifiable curve ) is equal to the same integral taken over an arbitrarily small circle around " a ".
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