Let $\displaystyle f(z)$ be a complex function defined on an open non-empty set $\displaystyle S$. Let $\displaystyle \gamma (t)$ be a contour wholly inside $\displaystyle S$. Does there exist another contour $\displaystyle \zeta (t)$ wholly inside $\displaystyle S$ with the property (abusing notation) that $\displaystyle \partial \gamma \subseteq I(\zeta)$ (meaning such that this contour lie strictly within this new contour).