While studying complex analysis a stumbled upon the following notation which is not clear to me what is it's definition (I couldn't even find it in my notes where my professor uses it extensively)
Given a curve $\gamma$, then we define $R(\gamma)$ as ...
For example I found it while studying Darboux theorem:
Theorem (Darboux): Let $\gamma: [a,b]\rightarrow \mathbb C$ be a regular curve with length $L_\gamma$. Let $f$ be continuous on $R(\gamma)$ then $$\left|\int_\gamma f(z)dz\right| \le L_\gamma \|f\|_\gamma$$ where $\|f\|_\gamma = \sup_\limits{z\,\in\, R(\gamma)}|f(z)|$
or the definition of the winding number:
Definition (Winding number): Let $\gamma$ be a closed curve, $a\in D$ but $a\notin R(\gamma)$, we call the winding number of $a$ with respect to $\gamma$ the quantity $$n(\gamma, a) = \frac{1}{2\pi i}\oint_\gamma\frac{\mathrm dz}{z-a}$$
And there're plenty of other examples but I think that from this two should be clear (not to me unfortunately) what $R(\gamma)$ is.
What I thought is that it could stand for one of this two $$R(\gamma)\equiv \operatorname{Int}(\gamma) \\ R(\gamma)\equiv \overline{\operatorname{Int}}(\gamma)$$ where $\operatorname{Int}(\gamma)$ is the domain upon which $\gamma$ is the boundary (the interior of $\gamma$), but I'm not really sure.
From context, it appears that $R(\gamma)$ is simply the range of the function $\gamma: [a,b] \to \mathbb{C}$. In other words, it's all the points that lie on the curve itself, not the interior or the closure of the interior.