Let $\mathcal{A}$ be a finite alphabet, and let $C$ be the Cantor space $\mathcal{A}^\omega$ under the product topology.

Given a finite string $s \in \mathcal{A}^*$, let $C(s)$ be the set of all strings in $\mathcal{A}^\omega$ that have $s$ as a prefix.

Is there a standard name for such sets $C(s)$ in $C$? If we think of $C$ as a Cantor set, then $C(s)$ is one the canonical "Cantor subsets".